Question

Consider the line y = 4x-3.
Find the equation of the line that is perpendicular to this line and passes through the point (3, -3).
Find the equation of the line that is parallel to this line and passes through the point (3, -3).

Answer 1

Answer:

perpendicular line: y = -$\frac{1}{4}$x - $\frac{9}{4}$

parallel line: y = 4x - 15

Step-by-step explanation:

Perpendicular line:

A perpendicular line to y = 4x-3 would have a slope that is the negative reciprocal (flip the fraction and add a negative sign). The negative reciprocal of 4 is - $\frac{1}{4}$.

Now that we have our slope, we can plug the given point of (3, -3) into the slope-intercept equation to find b.

-3 = - $\frac{1}{4}$(3) + b

-3 = - $\frac{3}{4}$ + b

Add $\frac{3}{4}$ to each side of the equation to isolate b.

-$\frac{9}{4}$ = b

Now we can write our equation, y = -$\frac{1}{4}$x - $\frac{9}{4}$

Parallel Line:

A parallel line to y = 4x-3 has the same slope. To find the equation, plug the slope and given point (3, -3) into the slope intercept equation and solve for b.

-3 = 4(3) + b

-15 = b

Now you can write the equation, y= 4x -15

Answer 2

Y=-1/4 I believe this is the correct answer....