Algebra 1 : Slope and Line Equations

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #151 : Equations Of Lines

Find the equation of the line that contains the points (4, 5) and (-2, -1).

Possible Answers:

Correct answer:

Explanation:

When finding the equation of a line given two points, we must first find the slope of the line.  To find the slope of a line in slope-intercept form

where m is the slope, we calculate

where  and  are the points.  Given the points, we can substitue. We get

Now that we know the slope, we can substitute the slope into the slope-intercept form

All we need to do now if find the value of b.  To do that, we will substitute one of the points into the equation.  Let's use (4, 5).  So,

So if we substitute the value of b into the slope-intercept form with the slope included, we get

which can also be written as 

Example Question #152 : Equations Of Lines

What is the equation of the line if the line connects the points  and ?

Possible Answers:

Correct answer:

Explanation:

If we chose to use the slope formula to determine a possible slope, we have:

Our slope becomes undefined.  The x-values will not change, and we are not able to write this in the slope-intercept form.

This line is a vertical line, and will be represented by  because the x-values will not change in a vertical line.

The answer is: 

Example Question #153 : Equations Of Lines

Determine the equation for the line, in slope intercept form, given a slope of  and that it passes through the point .

Possible Answers:

Correct answer:

Explanation:

To determine the equation for the line given only a point on the line and its slope, we can use point-slope form, which is given by the following:

, where  is the slope of the line and  is the point on the line.

Using the formula, we get

, which simplified becomes .

Example Question #154 : Equations Of Lines

What is the equation of a line with a slope of  and a y-intercept of ?

Possible Answers:

Correct answer:

Explanation:

Write the slope-intercept form for linear equations.

The  is the slope of the equation, and  is the y-intercept.

Substitute the values into the equation.

The equation of the line is:  

Example Question #155 : Equations Of Lines

Given the slope of a line is five, and a point on the graph is , write the equation of the line in point-slope form.

Possible Answers:

Correct answer:

Explanation:

Write the formula for point-slope form.

The variable  is the slope, and the point is in  format.  

Substitute all the givens.   There's is no need to simplify.

The answer is:  

Example Question #156 : Equations Of Lines

Given the slope is three, and a point is  on the graph, what is the equation of the line?

Possible Answers:

Correct answer:

Explanation:

Write the slope intercept form.

Substitute the slope and the point to find the y-intercept, .

Solve for the unknown variable.

Subtract nine from both sides.

Write the equation now that we have the slope and y-intercept.

The answer is: 

Example Question #157 : Equations Of Lines

Find the equation of the line given two points:   and 

Possible Answers:

Correct answer:

Explanation:

Write the slope intercept form.  The equation will be in this form.

Write the slope formula.

Let  and .  

Substitute the points into the slope formula.

The slope is:  

Use the slope and a given point, substitute them into the slope intercept form to find the y-intercept.

Solve for the y-intercept.

Add two-thirds on both sides.

Simplify both sides.

With the slope and y-intercept known, write the formula.

The answer is:  

Example Question #158 : Equations Of Lines

Given the x-intercept is seven, and the y-intercept is four, what is the equation of the line?

Possible Answers:

Correct answer:

Explanation:

The x-intercept is the value when .

The y-intercept is the value when .

We know the two points needed to find the equation of the line.

The points are:   and 

Use the slope formula to find the slope.

Write the slope-intercept equation.

Substitute the slope and the y-intercept.

The answer is:  

Example Question #61 : How To Find The Equation Of A Line

If the slope is four, and a known point is , what is the equation in point-slope form?

Possible Answers:

Correct answer:

Explanation:

Write the equation in point-slope form.

The variable  is the slope.  Substitute the slope and the point.

Simplify the right side of the equation.

The answer is:  

Example Question #1 : How To Find Slope Of A Line

What is the slope of the equation 4x + 3y = 7?

Possible Answers:

4/3

–3/4

3/4

–4/3

–7/3

Correct answer:

–4/3

Explanation:

We should put this equation in the form of y = mx + b, where m is the slope.

We start with 4x + 3y = 7.

Isolate the y term: 3y = 7 – 4x

Divide by 3: y = 7/3 – 4/3 * x

Rearrange terms: y = –4/3 * x + 7/3, so the slope is –4/3.

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