Question

Use the graph to answer the question

The graph shows a line passing through (-4, -5) and (4, 5)

Write the equation of the line shown in the graph in slope-intercept form

Answer 1

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

1. **Calculate the slope (m)** using the two points (-4, -5) and (4, 5):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - (-5)}{4 - (-4)} = \frac{5 + 5}{4 + 4} = \frac{10}{8} = \frac{5}{4}
\]

2. **Use one of the points to find the y-intercept (b)**. Let's use the point (4, 5):

We know the line has the form \(y = mx + b\). Plugging in \(m = \frac{5}{4}\) and the point (4, 5):

\[
5 = \frac{5}{4}(4) + b
\]
\[
5 = 5 + b
\]
\[
b = 5 - 5 = 0
\]

3. **Write the equation in slope-intercept form**:

Now that we have the slope and the y-intercept, we can write the equation:

\[
y = \frac{5}{4}x + 0
\]

This simplifies to:

\[
y = \frac{5}{4}x
\]

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

\[
y = \frac{5}{4}x
\]