Question

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

(-4,-5) (4,5)

(1 point)
The equation in slope-intercept form is y=blank fractionx

Answer 1

To write the equation of the line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b) from the points (-4, -5) and (4, 5).

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

The formula for the slope between two points (x₁, y₁) and (x₂, y₂) is:

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

Using the points (-4, -5) as (x₁, y₁) and (4, 5) as (x₂, y₂):

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

### Step 2: Use the slope to find the y-intercept (b)

Now that we have the slope, we can use one of the points to find the y-intercept. We can use the point (4, 5). The slope-intercept form is:

\[
y = mx + b
\]

Substituting the known values:

\[
5 = \frac{5}{4} \cdot 4 + b
\]

Calculating \(\frac{5}{4} \cdot 4\):

\[
5 = 5 + b
\]

Solving for b:

\[
5 - 5 = b
\]

\[
b = 0
\]

### Step 3: Write the equation

Now we can write the equation of the line in slope-intercept form:

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

Simplifying, we get:

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

Thus, the final answer is:

The equation in slope-intercept form is \(y = \frac{5}{4}x\).