Question

Consider the line y=−4/3x+3. Find the equation of the line that is parallel to this line and passes through the point , −4 6. Find the equation of the line that is perpendicular to this line and passes through the point , −4 6.

Answer 1

Answer:

The equation of the line parallel to y=4/3x−4 that passes through (-4,6) is y=4/3x−10/3 .

The equation of the line perpendicular to y=43x−4 that passes through (-4,6) is y=−3/4x+10 .

Step-by-step explanation:

Parallel means equal slopes. Hence, the slope of the line parallel to y=4/3x+3 is 4/3 . We know our slope and we know a point. We can therefore use point-slope form to determine the equation of the new line.  

y−y1=m(x−x1)  

y−6=4/3(x−4)  

y−6=4/3x−16/3  

y=4/3x−7/3  

The equation of the line parallel to y=4/3x−4 that passes through (-4,6) is y=4/3x−10/3 .

Question #2:

Perpendicular means negative reciprocal slopes. Hence, the slope perpendicular to y=4/3x+3 is y=−3/4 . We know our slope and we know a point. We can therefore use point-slope form to determine the equation of the new line.  

y−y1=m(x−x1)  

y−6=−3/4(x-4)  

y−6=−3/4x+6  

y=−3/4x+10

The equation of the line perpendicular to y=43x−4 that passes through (-4,6) is y=−3/4x+10 .