Activity
Find the equation of the line using point-slope form: ,
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Rewrite your equation from Question 1 in slope-intercept form.
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Find the equation of the line using point-slope form: ,
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y − 4 = 2(x + 1)
Rewrite your equation from Question 3 in slope-intercept form.
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Find the equation of the line using point-slope form: ,
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Rewrite your equation from Question 5 in slope-intercept form.
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Parallel lines are lines that have the same slope. Because they have the same slope, they will never touch, or intersect.
Find the equation of the line using point-slope form: ,
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Rewrite your equation from Question 7 in slope-intercept form.
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Use the graphing tool or technology outside the course.
Graph your equations from questions 2 and 4 on the same graph using the Desmos tool.
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Use the graphing tool or technology outside the course.
Graph your equations from questions 6 and 8 on the same graph using the Desmos tool.
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What is the same about the equations given in questions 2 and 4?
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The slopes are the same. They are both 2.
What is the same about the equations given in questions 6 and 8?
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The slopes are the same. They are both -4.
Self Check
Additional Resources
Find the Line Parallel to a Given Line
In this section, you will use what you know about writing the equation of a line given the slope and a point to write the equation of parallel lines. The graph shows the equation of the line The point is also plotted. You can use the fact that parallel lines have the same slope to find a line that is parallel to line and goes through point .
From the equation, you know the slope of the line is 2. The second line will pass through and have slope 2. To graph the line, start at and count out the rise and run. The slope is . Count out the rise, 2, and run, 1, and plot the point. You can graph the line as shown. Line is parallel to line and goes through point .
To find the equation of a line parallel to a line through a given point algebraically, you can use what you know about finding the equation of a line given the slope and a point.
Example
Write an equation of a line parallel to that contains the point . Write the equation in slope-intercept form.
Step 1 - Find the slope of the given line.
The line is in slope-intercept form
Step 2 - Find the slope of the parallel line
Parallel lines have the same slope
Step 3 - Identify the point
The given point is
Step 4 - Substitute values into the point-slope form
Simplify
Step 5 - Write the equation in slope-intercept form
Look at the graph with the parallel lines shown previously. Does this equation make sense? What is the -intercept of the line? What is the slope?
You can use this table as a reference for writing an equation of a line parallel to a given line.
Write the equation in slope-intercept form: .
Step 1 - Find the slope of the given line.
Step 2 - Find the slope of the parallel line.
Step 3 - Identify the point.
Step 4 - Substitute the values into the point-slope form: .
Step 5 - Simplify.
Step 6 - Write the equation in slope-intercept form: .
Try it
Try It: Find the Line Parallel to a Given Line
Write an equation of a line parallel to the line that contains the point . Write the equation in slope-intercept form.
Compare your answer:
Here is how to find a line parallel to a given line and point.
Step 1 - Find the slope of the given line.
Step 2 - Find the slope of the parallel line.
Step 3 - Identify the point.
Step 4 - Substitute the values into the point-slope form: .
Step 5 - Simplify.
Step 6 - Write the equation in slope-intercept form: .