Question

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

A coordinate plane going from negative 10 to 10 in increments of 1 labeled every 5 units on the x- and y-axes.
a line runs straight through the graph from the lower left quad to the upper right quad. there are two marked spaces that the line runs through: -4, -5 and 4, 5

(1 point)
The equation in slope-intercept form is $$
.

Answer 1

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

Given two points on the line:
- Point 1: (-4, -5)
- Point 2: (4, 5)

**Step 1: Calculate the slope (m)**

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

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

Substituting in the points:

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

**Step 2: Use one of the points to find the y-intercept (b)**

We can use the point (4, 5). We can substitute \( x = 4 \), \( y = 5 \), and \( m = \frac{5}{4} \) into the slope-intercept form to find \( b \):

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

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

Now we have the slope \( m = \frac{5}{4} \) and the y-intercept \( b = 0 \). Thus, the equation of the line is:

\[
y = \frac{5}{4}x + 0 \quad \text{or simply} \quad y = \frac{5}{4}x
\]

So, the equation in slope-intercept form is:

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