Question

Use the point-slope formula and the given points to choose the linear equation in slope-intercept form.

(8,5),(-4,-1)

Answer 1

To find the linear equation in slope-intercept form (y = mx + b) using the point-slope formula, we first need to determine the slope (m) between the two given points, (8, 5) and (-4, -1).

### 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:

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

Using the points \( (x_1, y_1) = (8, 5) \) and \( (x_2, y_2) = (-4, -1) \):

\[
m = \frac{-1 - 5}{-4 - 8} = \frac{-6}{-12} = \frac{1}{2}
\]

### Step 2: Use point-slope form
The point-slope form of the equation of a line is given by:

\[
y - y_1 = m(x - x_1)
\]

We can use either point; let's use the point (8, 5):

\[
y - 5 = \frac{1}{2}(x - 8)
\]

### Step 3: Simplify to slope-intercept form
Now, we simplify this equation to get it in slope-intercept form (y = mx + b):

1. Distribute \( \frac{1}{2} \):
\[
y - 5 = \frac{1}{2}x - 4
\]

2. Add 5 to both sides:
\[
y = \frac{1}{2}x - 4 + 5
\]

3. Combine the constants:
\[
y = \frac{1}{2}x + 1
\]

### Conclusion
The linear equation in slope-intercept form is:

\[
y = \frac{1}{2}x + 1
\]