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!~
