Write an equation of the line that passes through point P and is parallel to the line with the given equation. P(3,5); y=2x-6

y = -(5/2)x + 3 is a line perpendicular to y = (2/5)x + 2. This line is also perpendicular to y = (2/5)x + 9 because it has the same slope.

Step-by-step explanation:

A) So the line you are given is written in slope intercept form y = mx + b meaning that the slope of the line is  m = 2/5 and the intercept  b = 9 (so the line hits the y axis at 0,9). A line that is parallel has to have the same  slope so we know our m is the same. So we have y = (2/5)x + b. We need b. It passes (0, 2) since the x coordinate is 0 you know the y intercept is 2 but you can verify this using the point slope formula:

y - y1 = m(x - x1) plug in values

y - 2 = (2/5)(x - 0) now simplify

y - 2 = (2.5)x  last solve

y = (2/5)x + 2 see how when the x coordinate is 0 you can automatically use the point slope intercept formula? Neato!

B) Now we want a line perpendicular to y = (2/5)x + 2 and that passes through 0,3. What are the properties of a line perpendicular to a line of the form y = mx + b and passes through (0, 3)?  We know that the slope of this new line will be the reciprocal and have the opposite sign of m. So the new slope we will call it mnew = -(1/m) so plug in for m and you get mnew = -(1/[2/5]) if you simplify you get that the mnew = -(5/2). So we have half of our equation for the perpendicular: y = -(5/2)x + b. If you look at (0, 3) you see that the y intercept is 3 so b = 3. So:

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is