Question

Write an equation in slope-intercept form for the graph shown.



A coordinate plane with a line passing through points (0, negative 2) and (4, negative 1)

Answer 1

To write the equation of the line in slope-intercept form (y = mx + b), we first need to determine the slope (m) and the y-intercept (b).

1. **Calculate the slope (m):**
The formula for slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Using the points (0, -2) and (4, -1):
- \( (x_1, y_1) = (0, -2) \)
- \( (x_2, y_2) = (4, -1) \)

So the slope is:

\[
m = \frac{-1 - (-2)}{4 - 0} = \frac{-1 + 2}{4} = \frac{1}{4}
\]

2. **Identify the y-intercept (b):**
The y-intercept is the point where the line crosses the y-axis. From the given point (0, -2), we can see that:

\[
b = -2
\]

3. **Write the equation in slope-intercept form:**
Now that we have the slope (m = \(\frac{1}{4}\)) and the y-intercept (b = -2), we can write the equation:

\[
y = \frac{1}{4}x - 2
\]

Thus, the equation of the line in slope-intercept form is:

\[
y = \frac{1}{4}x - 2
\]