Writing equations of lines parallel and perpendicular to a given line through a point

Question

Consider the line

Find the equation of the line that is parallel to this line and passes through the point (3,  5)

Find the equation of the line that is perpendicular to this line and passes through the point  (3,  5)

Answer 1

Parallel lines have the same slope so this new line would have a slope of 2/3 and go through the point (3,5). You can use this slope and point to find the y-intercept. Slope-intercept form is the form of a linear equation that shows the slope (m) and y-intercept (b). You can use this form with the given information and find the y-intercept.

y=mx+b using 2/3 for slope (m) and (3,5) for (x,y)

5=2/3(3)+b

5=2+b

3=b

So the equation of the line parallel is y=2/3x+3

Perpendicular lines have the negative reciprocal slope so this new line would have a slope of -3/2 and go through the point (3,5). You can use this slope and point to find the y-intercept. Slope-intercept form is the form of a linear equation that shows the slope (m) and y-intercept (b). You can use this form with the given information and find the y-intercept.

y=mx+b using -3/2 for slope (m) and (3,5) for (x,y)

5=-3/2(3)+b

5=-4.5+b

9.5=b

So the equation of the line perpendicular is y=-3/2x+9.5.