Question

Write an equation in slope-intercept form for this graph.

y=

the points are, (4, 4) (-2, -5)

Answer 1

(-4, -2)*

Answer 2

To write the equation in slope-intercept form \(y = mx + b\), we first need to find the slope \(m\) using the two points given: (4, 4) and (-2, -5).

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 the points:

- \((x_1, y_1) = (4, 4)\)
- \((x_2, y_2) = (-2, -5)\)

We get:

\[
m = \frac{-5 - 4}{-2 - 4} = \frac{-9}{-6} = \frac{3}{2}
\]

Now that we have the slope \(m = \frac{3}{2}\), we can use one of the points to find the y-intercept \(b\). Let's use the point (4, 4). The equation in slope-intercept form is:

\[
y = mx + b
\]

Substituting \(m\) and the point (4, 4):

\[
4 = \frac{3}{2}(4) + b
\]

Calculating the right side:

\[
4 = 6 + b
\]

Now, solve for \(b\):

\[
b = 4 - 6 = -2
\]

Now that we have both \(m\) and \(b\), we can write the final equation in slope-intercept form:

\[
y = \frac{3}{2}x - 2
\]

Answer 3

It seems you would like to determine the equation in slope-intercept form using the points (4, 4) and (-4, -2). Let's do that step-by-step.

### Step 1: Find the slope \(m\) using the points (4, 4) and (-4, -2).

Using the slope formula:

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

Substituting the points:

- \((x_1, y_1) = (4, 4)\)
- \((x_2, y_2) = (-4, -2)\)

We get:

\[
m = \frac{-2 - 4}{-4 - 4} = \frac{-6}{-8} = \frac{3}{4}
\]

### Step 2: Use the slope and one point to find the y-intercept \(b\).

Let's use the point (4, 4) to find \(b\).

We know the equation is:

\[
y = mx + b
\]

Substituting \(m\) and the point (4, 4):

\[
4 = \frac{3}{4}(4) + b
\]

Calculating the right side:

\[
4 = 3 + b
\]

Now, solve for \(b\):

\[
b = 4 - 3 = 1
\]

### Final Step: Write the equation in slope-intercept form.

With \(m = \frac{3}{4}\) and \(b = 1\), the equation is:

\[
y = \frac{3}{4}x + 1
\]

This is the equation in slope-intercept form for the line that passes through the points (4, 4) and (-4, -2).