# Common Core: High School - Statistics and Probability : Interpret Slope and Intercept of a Linear Model: CCSS.Math.Content.HSS-ID.C.7

## Example Questions

### Example Question #1 : Interpret Slope And Intercept Of A Linear Model: Ccss.Math.Content.Hss Id.C.7

A professor conducts a study on the relationship between sleep and academic performance by asking his 420 students how many hours of sleep they missed while studying for the class final.

The regression output is as follows:

Which of the following statements is TRUE?

The average score on the final is 698.8 points.

For every additional hour of sleep missed, the number of points scored on the final decreases by 2.28 points.

The regression equation itself proves that the results are statistically significant.

Sleep has no effect on academic performance.

The average score on the final is 696.52 points.

For every additional hour of sleep missed, the number of points scored on the final decreases by 2.28 points.

Explanation:

### Example Question #1 : Interpret Slope And Intercept Of A Linear Model: Ccss.Math.Content.Hss Id.C.7

Identify the slope of the following line:

Explanation:

This question asks us to analyze the constituent components of a linear equation written in the slope intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

The slope is commonly defined as rise over run. In other words it is the change in y-values across points divided by the change in x-values. It is calculated using the following formula:

In this formula, the x and y-values come from two points from the line written in the following format:

It is important to note that slopes can be positive or negative. A positive slope moves upward from left to right while a negative slope moves downward.

Now, lets solve the problem. We will start by identifying two points on the line. Lets observe the point where the line crosses the x-axis and the point to where it crosses , positive five, on the x-axis.

These two points are:

Now, substitute these numbers into the slope formula.

The slope is positive because the line moves upward from left to right.

We find that the slope of the equation is one. We can also calculate the slope by using the traditional "rise over run" definition. If we count blocks on the graph we can see that for every six blocks that it "rises," it "runs" six blocks. In other words, the slope increases one block in the x-direction as it increases one block in the y-direction; therefore, the slope is one (see figure below).

### Example Question #159 : Interpreting Categorical & Quantitative Data

Identify the y-intercept of the following line:

Explanation:

This question asks us to analyze the constituent components of a linear equation written in the slope-intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

The y-intercept represents the point where the line intersects the y-axis. We can identify the y-intercept by locating it on the graph (see the red circle in the figure below).

The y-intercept is located at the following point:

They correct y-intercept is as follows:

### Example Question #160 : Interpreting Categorical & Quantitative Data

Identify the slope of the following line:

Explanation:

This question asks us to analyze the constituent components of a linear equation written in the slope-intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

The slope is commonly defined as rise over run. In other words, it is the change in y-values across points divided by the change in x-values. It is calculated using the following formula:

In this formula, the x- and y-values come from two points from the line written in the following format:

It is important to note that slopes can be positive or negative. A positive slope moves upward from left to right while a negative slope moves downward.

Now, lets solve the problem. We will start by identifying two points on the line. Lets observe the point where the line crosses the x-axis and the point to where it crosses , positive five, on the x-axis.

These two points are:

Now, substitute these numbers into the slope formula.

The slope is positive because the line moves upward from left to right.

We have calculated that the slope of the equation is one. We can also calculate the slope by using the traditional "rise over run" definition. If we count blocks on the graph, then we can see that for every six blocks that it "rises," it "runs" six blocks. In other words, the slope increases one block in the x-direction as it increases one block in the y-direction; therefore, the slope is one (see figure below).

### Example Question #1 : Interpret Slope And Intercept Of A Linear Model: Ccss.Math.Content.Hss Id.C.7

Identify the slope of the following line:

Explanation:

This question asks us to analyze the constituent components of a linear equation written in the slope-intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

The slope is commonly defined as rise over run. In other words, it is the change in y-values across points divided by the change in x-values. It is calculated using the following formula:

In this formula, the x- and y-values come from two points from the line written in the following format:

It is important to note that slopes can be positive or negative. A positive slope moves upward from left to right while a negative slope moves downward.

Now, lets solve the problem. We will start by identifying two points on the line.

These two points are:

Now, substitute these numbers into the slope formula.

The slope is positive because the line moves upward from left to right.

We have calculated that the slope of the equation is 13 We can also calculate the slope by using the traditional 'rise over run' definition. If we count blocks on the graph, then we can see that for every 52 blocks that it 'rises', it 'runs' 4 blocks. In other words, the slope increases one block in the x-direction as it increases 13 block in the y-direction; therefore, the slope is 13 (see figure below)

### Example Question #2 : Interpret Slope And Intercept Of A Linear Model: Ccss.Math.Content.Hss Id.C.7

Identify the slope of the following line:

Explanation:

This question asks us to analyze the constituent components of a linear equation written in the slope-intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

The slope is commonly defined as rise over run. In other words, it is the change in y-values across points divided by the change in x-values. It is calculated using the following formula:

In this formula, the x- and y-values come from two points from the line written in the following format:

It is important to note that slopes can be positive or negative. A positive slope moves upward from left to right while a negative slope moves downward.

Now, lets solve the problem. We will start by identifying two points on the line.

These two points are:

Now, substitute these numbers into the slope formula.

The slope is positive because the line moves upward from left to right.

We have calculated that the slope of the equation is 7 We can also calculate the slope by using the traditional 'rise over run' definition. If we count blocks on the graph, then we can see that for every 28 blocks that it 'rises', it 'runs' 4 blocks. In other words, the slope increases one block in the x-direction as it increases 7 block in the y-direction; therefore, the slope is 7 (see figure below)

### Example Question #3 : Interpret Slope And Intercept Of A Linear Model: Ccss.Math.Content.Hss Id.C.7

Identify the slope of the following line:

Explanation:

This question asks us to analyze the constituent components of a linear equation written in the slope-intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

The slope is commonly defined as rise over run. In other words, it is the change in y-values across points divided by the change in x-values. It is calculated using the following formula:

In this formula, the x- and y-values come from two points from the line written in the following format:

It is important to note that slopes can be positive or negative. A positive slope moves upward from left to right while a negative slope moves downward.

Now, lets solve the problem. We will start by identifying two points on the line.

These two points are:

Now, substitute these numbers into the slope formula.

The slope is positive because the line moves upward from left to right.

We have calculated that the slope of the equation is 11 We can also calculate the slope by using the traditional 'rise over run' definition. If we count blocks on the graph, then we can see that for every 44 blocks that it 'rises', it 'runs' 4 blocks. In other words, the slope increases one block in the x-direction as it increases 11 block in the y-direction; therefore, the slope is 11 (see figure below)

### Example Question #4 : Interpret Slope And Intercept Of A Linear Model: Ccss.Math.Content.Hss Id.C.7

Identify the slope of the following line:

Explanation:

This question asks us to analyze the constituent components of a linear equation written in the slope-intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

The slope is commonly defined as rise over run. In other words, it is the change in y-values across points divided by the change in x-values. It is calculated using the following formula:

In this formula, the x- and y-values come from two points from the line written in the following format:

It is important to note that slopes can be positive or negative. A positive slope moves upward from left to right while a negative slope moves downward.

Now, lets solve the problem. We will start by identifying two points on the line.

These two points are:

Now, substitute these numbers into the slope formula.

The slope is positive because the line moves upward from left to right.

We have calculated that the slope of the equation is 5 We can also calculate the slope by using the traditional 'rise over run' definition. If we count blocks on the graph, then we can see that for every 20 blocks that it 'rises', it 'runs' 4 blocks. In other words, the slope increases one block in the x-direction as it increases 5 block in the y-direction; therefore, the slope is 5 (see figure below)

### Example Question #5 : Interpret Slope And Intercept Of A Linear Model: Ccss.Math.Content.Hss Id.C.7

Identify the slope of the following line:

Explanation:

This question asks us to analyze the constituent components of a linear equation written in the slope-intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

m=\textup{slope}

The slope is commonly defined as rise over run. In other words, it is the change in y-values across points divided by the change in x-values. It is calculated using the following formula:

m=\frac{\Delta y}{\Delta x}

m=\frac{y_2-y_1}{x_2-x_1}

In this formula, the x- and y-values come from two points from the line written in the following format:

(x,y)

It is important to note that slopes can be positive or negative. A positive slope moves upward from left to right while a negative slope moves downward.

Now, lets solve the problem. We will start by identifying two points on the line.

These two points are:

\left( -2 , -15 \right) and \left( 2 , 53 \right)

Now, substitute these numbers into the slope formula.

\\ \\ m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{ 53 - -15 }{ 2 - -2 } \\ \\ m=\frac{ 68 }{ 4 } \\ \\ m= 17.0

The slope is positive because the line moves upward from left to right.

We have calculated that the slope of the equation is 17 We can also calculate the slope by using the traditional 'rise over run' definition. If we count blocks on the graph, then we can see that for every 68 blocks that it 'rises', it 'runs' 4 blocks. In other words, the slope increases one block in the x-direction as it increases 17 block in the y-direction; therefore, the slope is 17 (see figure below)

### Example Question #6 : Interpret Slope And Intercept Of A Linear Model: Ccss.Math.Content.Hss Id.C.7

Identify the slope of the following line:

Explanation:

This question asks us to analyze the constituent components of a linear equation written in the slope-intercept formula:

This formula provides information about two key parts of a line: the slope and y-intercept.

The slope is commonly defined as rise over run. In other words, it is the change in y-values across points divided by the change in x-values. It is calculated using the following formula:

In this formula, the x- and y-values come from two points from the line written in the following format:

It is important to note that slopes can be positive or negative. A positive slope moves upward from left to right while a negative slope moves downward.

Now, lets solve the problem. We will start by identifying two points on the line.

These two points are:

Now, substitute these numbers into the slope formula.

The slope is positive because the line moves upward from left to right.

We have calculated that the slope of the equation is 10 We can also calculate the slope by using the traditional 'rise over run' definition. If we count blocks on the graph, then we can see that for every 40 blocks that it 'rises', it 'runs' 4 blocks. In other words, the slope increases one block in the x-direction as it increases 10 block in the y-direction; therefore, the slope is 10 (see figure below)