Question

Use the line on the graph to write an equation that represents the function.

y = x+

Answer 1

y = -3x - 1

Explanation:

We can represent the given line using an equation in slope-intercept form

`y = mx+b`

In this form,
`m` is the line's slope, and
`b` is the y-coordinate of the point on the line when it touches the y-axis (its y-intercept).

First, we can solve for the line's slope using two points on the line and the formula m = rise / run. We can use the points (0, -1) and (1, -4), whose coordinates correspond to (x₁, y₁) and (x₂, y₂).

`m = \frac{\textrm{rise}}{\textrm{run}} = (y_2 - y_1)/(x_2 - x_1)`

`m = (-4 - (-1))/(1 - 0)`

`m = (-4 + 1)/(1)`

`m = -3`

So, the slope (m) of this line is -3.

We can plug that value into the model for slope-intercept form.

y = -3x + ▢

Now, we have to identify the line's y-intercept (the point on the line when it touches the y-axis). It is (0, -1). Finally, we can put the y-coordinate of that point into slope-intercept form equation.

y = -3x - 1