Question

Write a system of linear equations for the graph below

Answer 1

Answer:

y = -3x + 3

$y=\frac{1}{3}x-7$

Step-by-step explanation:

Slope of a line passing through two points ($x_1, y_1$) and $(x_2, y_2)$ is determined by the formula,

Slope = $\frac{(y_2-y_1)}{(x_2-x_1)}$

If these points are (0, 3) and (3, -6),

Slope of the line passing through these lines = $\frac{3+6}{0-3}$ = (-3)

Equation of the line which passes through (0, 3) and slope = (-3),

y - y' = m(x - x')

y - 3 = (-3)(x- 0)

y - 3 = -3x

y = -3x + 3

Now slope of another line that passes through (3, -6) and (0, -7),

m' = $\frac{(-6+7)}{(3-0)}$

m' = $\frac{1}{3}$

Equation of the line that passes through (0, -7) and slope = $\frac{1}{3}$

y - (-7) = $\frac{1}{3}(x-0)$

y + 7 = $\frac{1}{3}x$

y = $\frac{1}{3}x-7$

Therefore, system of linear equations are,

y = -3x + 3

$y=\frac{1}{3}x-7$