Question

Write an equation that represents the line.
Use exact numbers.

Answer 1

`y = (4)/(5) x -3(3)/(5)`

Explanation:

Finding slope

Slope-intercept formula: y = mx + b

Two good points on the graph:

(2, -2)

(-3, -6)

Two-point slope formula:

`(y_2-y_1)/(x_2-x_1)`

Plug these points into the graph:

`(-6-(-2))/(-3-2)` solve

`=(-4)/(-5)` simplify

`=(4)/(5)` a negative divided by a negative is a positive

m = 4/5

Finding y-intercept

The y-intercept is the point where the line of the graph goes through the y-axis. And when x is 0. In this graph, we have a point in between -3 and -4, but closer to -4. But is nearer to -4, so we will approximate:

b = (0, -3 3/5)

The equation

The last step is setting up the equation. We are using slope-intercept: y= mx + b

Plugin the values for m and b

y = mx + b

y = 4/5x - 3 3/5 (note that since it is negative, which has a minus sign, it replaces the +.

Answer 2

y = 4/5x - 18/5

or y = 4/5x - 3 3/5

or y = 1/5(4x - 18)

Explanation:

Slope: m = (y2-y1)/(x2-x1)

Use coordinates (-3, -6) and (2, -2)

m = (-2 - -6)/(2 - -3) = (-2 + 6)/(2 + 3) = 4/5

so y = mx + b

Using coordinate (-3, -6)

-6 = 4/5(-3) + b

-6 = -12/5 + b

b = -6 + 12/5 = -30/5 + 12/5 = - 18/5 = -3 3/5

y = 4/5x - 3 3/5