Question

Find the equation of the line passing through the point (6,3) that is perpendicular to the line 4x−5y=−10.

Answer 1

Hi there! :)

Line passes through (6, 3) & perpendicular to 4x - 5y = -10

Step 1:

Identify the slope, In the slope-intercept form y=mx+b, we know that "m" is our slope.

We need to isolate y so we must first subtract 4x from both sides.

-5y = -4x - 10

Divide both sides by -5.

y = (-4x - 10)/-5

Simplify.

y = 4/5x + 2

"M" is simply a place mat so if we look at our given line, the "m" value is 4/5. Therefore, the slope for our given line is 4/5.

We need to note that we're looking for a line that's perpendicular to the given one. This means that our new line is the negative reciprocal of the given slope. This means that our new lines slope is -5/4.

Step 2:

Use point-slope form ( y-y₁=m(x-x₁) ) to complete our task of finding the y-intercept of our new line (which goes through 6,3).

y-y₁=m(x-x₁)

Let's start by plugging in -5/4 for m (our slope), 6 for x1 and 3 for y1.

y - (3) = -5/4(x - 6)

Simplify.

y - 3 = -5/4x + 5/6

Simplify by adding 3 from both sides.

y = -5/4x + 4 1/6

This can also be written as: y = -5/4x + 25/6

This means that step 2's answer is: the y-intercept is 25/6

Step 3's answer is:

y = -5/4x + 25/6

~Hope I helped!~