|c|c|c|
Line & Slope & y-intercept
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y= - 2/5x+ 6& - 2/5 & 6 [0.8em]
If we multiply the slopes of two perpendicular lines, the product equals -1. With this information, we can find the slope of the perpendicular line.
The slope of the perpendicular line is 52.
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Perpendicular Line & Slope & y-intercept
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y= 5/2x+ b& 5/2 & b [0.8em]
To complete the equation, we also have to find the line's y-intercept. Notice that the y-intercept is a point on the y-axis which means its x-coordinate is 0. Since we know that the perpendicular line goes through (0,-3) we know that the y-intercept is at -3. Now we can complete the equation.
y= 5/2x-3
Let's plot the graph of both equations. Since they are perpendicular, they will intersect at a right angle.
bParallel lines have the same slope but different y-intercepts. To find the slope of the line, we must write it in slope-intercept form.
Now we can identify the line's slope and y-intercept.
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Line & Slope & y-intercept
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y= 3/2x+ 5& 3/2 & 5 [0.8em]
As already explained, if two lines are parallel, they have to have the same slope but different y-intercepts. Therefore, we know that the parallel line must have a slope of 32.
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Parallel Line & Slope & y-intercept
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y= 3/2x+ b& 3/2 & b [0.8em]
Like in Part A, we see that the given point has an x-coordinate of 0. This means the points y-coordinate describes the line's y-intercept. With this information, we can write the line's equation.
y=3/2x+7
If we plot both lines, we see that they are parallel.
