What is the equation of the line that is perpendicular to the line y=3/4x−6 and passes through the point (−3,5

Answer 1

The line y = 3/4x - 6 has a slope of 3/4. A line perpendicular to 3/4 has a slope of -4/3. So the slope of our new line will be -4/3.

We are told that the line goes through the point (-3, 5). That is x = -3 and y = 5. Now that we know a point and a slope, we can use the formula y2 - y1 = m(x2 - x1).

(x1, y1) = (-3, 5)

x1 = -3

y1 = 5

m = slope = -4/3

the general line equation is y2 - y1 = m(x2 - x1)

y2 - 5 = -4/3(x2 - (-3))

y2 - 5 = -4/3(x2 + 3)

y2 - 5 = -4/3(x2 + 3)

y2 - 5 = -4/3·x2 - 4

y2 = -4/3·x2 + 1

or simply y = (4/3)x + 1

Finished !!

Answer 2

The line y = 3/4x - 6 has a slope of 3/4. We want to find a perpendicular line. To find the perpendicular slope, we want to find the negative reciprocal of 3/4. Basically, we want to flip the fraction over and make it negative. So our new slope will be -4/3.

We also know that we want our line to go through the point (-3, 5). Now that we know a point and a slope, we can use the formula y - y₁ = m(x - x₁).

(x₁, y₁) = (-3, 5)

x₁ = -3

y₁ = 5

m = slope = -4/3

y - y₁ = m(x - x₁)

y - 5 = -4/3(x - (-3))

y - 5 = -4/3(x + 3)

This is the equation in point-slope form! However, your teacher might want the equation in a specific form.

For example, to write it in intercept form, we need to multiply on the right-hand side, and then add 5 to both sides.

y - 5 = -4/3(x + 3)

y - 5 = -4/3·x - 4

y = -4/3·x + 1