Question

How do you write an equation for this graph?

Answer 1

see explanation

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

(7) left

to find slope m use the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (0, - 5) and (x₂, y₂ ) = (- 2, - 1) ← 2 points on the line

m =
`(-1-(-5))/(-2-0)` =
`(-1+5)/(-2)` =
`(4)/(-2)` = - 2

the line crosses the y- axis at (0, - 5 ) ⇒ c = - 5

y = - 2x - 5 ← equation of line

(7) right)

find slope m with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (2, - 3) ← 2 point on line

m =
`(-3-3)/(2-0)` =
`(-6)/(2)` = - 3

the line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = - 3x + 3 ← equation of line

(8)

5y + 22 = 5x - 33 ( subtract 22 from both sides )

5y = 5x - 55 ( divide through by 5 )

y = x - 11 ← in slope- intercept form

that is option A