Write The Equation Of The Following...

Question

Write the equation of a line with x-intercept 4 perpendicular to the line y= -3x+7

 

Write the equation of the line with y-intercept -7 that is perpendicular to the line passing through (-3, 9) and (7, -5)

 

Write the equation of the line containing (5, -3) that is parallel to the line through (8, -12) and (-84, 3)

 

Answer 1

Hi Madison,

 

 

Write the equation of a line with x-intercept 4 perpendicular to the line y= -3x+7

Write the equation of the line with y-intercept -7 that is perpendicular to the line passing through (-3, 9) and (7, -5)

Write the equation of the line containing (5, -3) that is parallel to the line through (8, -12) and (-84, 3)

 

question 1)  Write the equation of a line with x-intercept 4 perpendicular to the line y= -3x+7

 

A perpendicular line has a slope which is the negative reciprocal.  So the slope =1/3

 

An x-intercept 4 would be the point (4,0)

 

Using slope intercept form y=mx+b

Substutue in the slope     y=1/3x+b

Substitute in point (4,0) to find the b which is the y-intercept

0=1/3(4)+b

0=4/3+b

-4/3=b

 

ANSWER:  y=1/3x-4/3

 

Question 2) Write the equation of the line with y-intercept -7 that is perpendicular to the line passing through (-3, 9) and (7, -5)

 

First find the slope of the original line

 

9-(-5)     14      7

------=  ----= ----

-3-7       -10    -5

 

A line that is perpendicular has a slope which is the negative reciprocal:  5/7

 

y-intercept -7 is b

 

ANSWER:  y=5/7x-7

 

 

Question 3)   Write the equation of the line containing (5, -3) that is parallel to the line through (8, -12) and (-84, 3)

 

 

Parallel lines have the same slope.

 

-12-3     -15

------ =  -----

8-(-84)    92

 

 

y=-15/92x+b

 

Substitute in point (5, -3)

 

-3=-15/92(5)+b

-3=-75/92+b

-201/92=b

 

 

ANSWER:  y=-15/92x-201/92

 

That's all three questions answered...