Question

Which equation has a graph that goes through the points (4, -6) and (0, 6)?

Answer 1

Answer:

$y = -3x + 6$

Step-by-step explanation:

Find the gradient of the equation

$\frac{Difference in y}{Difference in x} \\\\\frac{6 - - 6}{0 - 4} = \frac{12}{-4} = -3$

The equation will have the gradient -3x

Use the general equation of a line, and substitute the coordinates in to find the y-intercept.

$y = x + c\\ y = -3x + c$

(4, -6)

$-6 = -3(4) + c\\ -6 = -12 + c\\ -6 + 12 = c\\ c = 6$$6 = -3(0) + c\\ 6 = 0 + c\\ c = 6$

(0, 6)

$6 = -3(0) + c\\ 6 = -0 + c\\ c = 6$

The equation of the line is

$y = -3x + 6$