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.

Courtney C.
06/30/22
Katie F.
Thank you so much!!!06/30/22