Algebra 1 : Slope and Line Equations

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #133 : Equations Of Lines

Using the data above, find an equation for the line that passes through these points and the -intercept. 

Possible Answers:

Correct answer:

Explanation:

The data provided is enough data to for us to find the equation of a line that passes through these points: 

.

An equation representing a line: 
,

where m = slope, b = y-intercept.

To find the slope use the following formula, 

,

so in this problem the slope: 

.

The y-intercept is given. From this slope that is found, we see that the numerator is zero, this means that there is no slope, thus the line must be a horizontal line.

Our formula then is:

Example Question #134 : Equations Of Lines

Given the points  and .

Find the slope-intercept form of the line that contains these points.

Possible Answers:

Correct answer:

Explanation:

Use the given points and plug them into slope formula:

Remember points are written in the following format:

 Substitute.

Now, that we have the slope of the line we can insert values into the point-slope formula:

Distribute the fraction through the quantity on the left side of the equation.

 

Add  to both sides.

The slope-intercept form is written as:

Where  is the slope and  is the y-intercept.

In our equation our slope is  and our y-intercept is .

The equation of the line that contains these points is:

 

Simplify.

Example Question #135 : Equations Of Lines

Write the slope-intercept form of the equation of the line described.

Passes through the point , perpendicular to .

Possible Answers:

Correct answer:

Explanation:

The slope-intercept equation of a line is in the form .

A line that is perpendicular has a slope that is the opposite reciprocal of the given line. 

Slope of perpendicular line: 

Using the point slope formula,

where  

we get the following equation.

Example Question #136 : Equations Of Lines

Find the equation of the line with a slope of 2 that passes through the point (4,6).

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we need to remember point-slope formula:

Then we plug in m=2 and (x1,y1)=(4,6) and solve:

Example Question #137 : Equations Of Lines

Find the equation of the line with slope 1/3 running through the point (15,2).

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we need to remember point-slope formula:

Then we plug in m=1/3 and (x1,y1)=(15,2) and solve:

Example Question #138 : Equations Of Lines

Find the equation of the line with slope 4 running through the point (-1,-5).

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we need to remember point-slope formula:

Then we plug in m=4 and (x1,y1)=(-1,-5) and solve:

Example Question #139 : Equations Of Lines

Find the equation of the line with slope -3 running through the point (2,5).

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we need to remember point-slope formula:

Then we plug in m=2 and (x1,y1)=(4,6) and solve:

Example Question #140 : Equations Of Lines

Find the equation of the line with slope -1 running through the point (2,-2).

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we need to remember point-slope formula:

Then we plug in m=-1 and (x1,y1)=(2,-2) and solve:

Example Question #141 : Equations Of Lines

Find the equation of the line with slope 1/2 running through the point (-8,2).

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we need to remember point-slope formula:

Then we plug in m=1/2 and (x1,y1)=(-8,2) and solve:

Example Question #142 : Equations Of Lines

Find the equation of the line with slope -2 running through the point (1,3).

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we need to remember point-slope formula:

Then we plug in m=-2 and (x1,y1)=(1,3) and solve:

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