Activity
Answer the following questions.
Use the graph below to pick two points and find the slope between the two points.
Compare your answer:
The slope of the line is .
Use your two points in the slope formula to confirm the slope is correct.
Compare your answer:
Your answer may vary, but here is a sample.
Using the slope and a point, write your equation in point-slope form.
Compare your answer:
Your answer may vary, but here is a sample.
and
becomes: .
Now write your equation in slope-intercept form.
Compare your answer:
Convert slope-intercept form to standard form.
Compare your answer:
Look at your equation and the original graph. What do you notice? How can you use a graph to check your equation?
Compare your answer:
Your answer may vary, but here is a sample.
The -intercept of the graph is and the slope is .
Self Check
Additional Resources
Find an Equation of the Line Given Two Points
So far, you have two options for finding an equation of a line: slope-intercept or point-slope. When you start with two points, it makes more sense to use the point-slope form.
But then you need the slope. You can find the slope with just two points and then use it and one of the given points to find the equation.
Example
Write the equation of a line that contains the points and . Write the equation in slope-intercept form and standard form.
Step 1 - Find the slope using the given points.
Find the slope of the line through and .
Step 2 - Choose one point.
Choose either point.
Step 3 - Substitute the values into the point-slope form, .
Simplify
Step 4 - Write the equation in slope-intercept form.
Step 5 - Convert slope-intercept form to standard form.
Use this table for easy reference to find an equation of a line given two points.
Step 1 - Find the slope using the given points.
Step 2 - Choose one point.
Step 3 - Substitute the values into the point-slope form: .
Step 4 - Write the equation in slope-intercept form.
Step 5 - Convert slope-intercept form to standard form.
To find an equation of a line given the slope and a point, follow these steps:
Step 1 - Identify the slope.
Step 2 - Identify the point.
Step 3 - Substitute the values into the point-slope form, .
Step 4 - Write the equation in slope-intercept form.
Step 5 - Convert slope-intercept form to standard form.
Try it
Try It: Writing the Equation of a Line Given Two Points
Write the equation of a line that contains the points and .
Here is how to find an equation of a line that contains the points and .
Again, the first step will be to find the slope.
Step 1 - Find the slope of the line through and .
Step 2 -
Step 3 -
Step 4 -
A line with undefined slope is a vertical line. Both given points have an -coordinate of . So, the equation of the line is . There is no , so the equation cannot be written in slope-intercept form.