Question

Write an equation to represent this graph in slope-intercept form

y = 1/2 * x + 2

y = 2x + 1/2

y = - 2x - 2

y = 1/2 * x - 2

The slope intercept is (-1,0) and (0,-2)

Answer 1

To find an equation that represents the line that passes through the points (-1, 0) and (0, -2) in slope-intercept form (y = mx + b), we need to calculate the slope (m), then use one of the points to solve for b (the y-intercept).

1. **Calculate the slope (m)** using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points (-1, 0) and (0, -2):

\[
m = \frac{-2 - 0}{0 - (-1)} = \frac{-2}{1} = -2
\]

2. **Use one of the points** (we can use (0, -2) because it’s already at the y-intercept) to find b. The y-intercept (b) is the value of y when x = 0:

Hence, from the point (0, -2):

\[
b = -2
\]

3. **Write the equation** in slope-intercept form using m and b:

\[
y = -2x - 2
\]

So the equation that represents the graph is

\[
\boxed{y = -2x - 2}
\]

This matches the option given in your list.