Algebra 1 : How to find the equation of a line

Study concepts, example questions & explanations for Algebra 1

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Example Questions

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

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 #152 : 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 #153 : 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 #62 : How To Find The Equation Of A Line

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 #155 : 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 #156 : 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 #157 : 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 #158 : Equations Of Lines

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 #161 : Equations Of Lines

A line passes through the points (3, 9) and (5, 3), and has a y-intercept of 3.  Which of the following is an equation for that line?

Possible Answers:

 

Correct answer:

 

Explanation:

The equation for a line is always , where  and .

Given two data points, we are able to find the slope, m, using the formula 

.

Using the data points provided, our formula will be: 

, which gives us  or , .

Our y-intercept is given.

Thus our equation for the line containing these points and that y-intercept is .

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