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).

perpendicular line: y = -x -

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 - .

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

-3 = - (3) + b

-3 = - + b

Add to each side of the equation to isolate b.

- = b

Now we can write our equation, y = -x -

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

the final function for the graph becomes x-2=-1. before graphing you solve the equation, where x=1. then graph accordingly.   ( on the x-axis, 1 on the line will possess a vertical line.)