Find the value of r so that the line passes through (6, -2) and (4,r) has a slope of -3

Hello from MrBillDoesMath!

r = 4

Discussion:

Slope of a non-vertical line = (change in y values)/(change in x values)

In our case this becomes

slope = -3                 =>

-3 = ( r-(-2))/(4 - 6)     => as 4 -6 = -2

-3 = ( r+2)/(-2)            => multiply both sides by -2

-3(-2) = r+2                 =>

6 = r + 2                   => subtract 2 from both sides

r = 6 - 2 = 4

Thank you,

MrB

step-by-step explanation:

f(x)=2x^2 -1 

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved  up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1