Please help me write the equation of a line that passes through the point ( -1, 5) and has a slope of -7

y = -7x - 2

Step-by-step explanation:

use y = mx + b

y = y-coordinate = 5

m = slope = -7

x = x-coordinate = -1

b = y-intercept = the only missing piece/what we're solving

usually, for an equation, x and y stay as variables, but to find the y intercept we need to plug in the coordinates:

5 = (-7)(-1) + b                   multiply -7 and -1

5 = 7 + b                           subtract 7 from both sides

b = -2                              

plug b into the equation and leave x and y as variables:

y = -7x - 2

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240