Question

Write a system of linear equations for the graph below

Answer 1

y = -3x + 3

`y=(1)/(3)x-7`

Explanation:

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

Slope =
`((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 =
`(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' =
`((-6+7))/((3-0))`

m' =
`(1)/(3)`

Equation of the line that passes through (0, -7) and slope =
`(1)/(3)`

y - (-7) =
`(1)/(3)(x-0)`

y + 7 =
`(1)/(3)x`

y =
`(1)/(3)x-7`

Therefore, system of linear equations are,

y = -3x + 3

`y=(1)/(3)x-7`