Question

Use the graph to answer the 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.

(1 point)
The equation in slope-intercept form is $$
The points on the graph are (-4, -5) and (4, 5)

Answer 1

To find the equation of the line in slope-intercept form \( y = mx + b \), we need to calculate the slope \( m \) using the two given points \((-4, -5)\) and \( (4, 5)\).

1. **Calculate the slope (m)**:
The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Plugging in the values:
- \( (x_1, y_1) = (-4, -5) \)
- \( (x_2, y_2) = (4, 5) \)

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

2. **Use the slope and a point to find the y-intercept (b)**:
We can use one of the points to find the y-intercept. Let's use the point \((4, 5)\):
\[
y = mx + b
\]
Plugging in the slope and the coordinates of the point:
\[
5 = \frac{5}{4}(4) + b
\]
\[
5 = 5 + b
\]
\[
b = 5 - 5 = 0
\]

3. **Write the equation in slope-intercept form**:
Now we can write the equation of the line:
\[
y = \frac{5}{4}x + 0
\]
or simply:
\[
y = \frac{5}{4}x
\]

Thus, the equation of the line in slope-intercept form is \( y = \frac{5}{4}x \).