Question

A line passing through the points (6, –2) and (–2, 4).

Complete the work shown:

1. Use slope formula to find the slope.

2. Substitute a point and slope in point-slope form.

3. Distribute the slope through the parentheses.

4. Solve for the y-variable.

1. m = StartFraction 4 minus (negative 2) Over negative 2 minus 6 EndFraction = StartFraction 6 Over negative 8 EndFraction = negative three-fourths. 2. y minus 4 = negative three-fourths (x minus (negative 2)). 3. y minus 4 = negative three-fourths x minus three-halves.

4. y = negative three-fourths x +

Answer 1

Let's go through each step systematically.

### 1. Use slope formula to find the slope.
The slope formula is given by:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \((6, -2)\) and \((-2, 4)\):

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

### 2. Substitute a point and slope in point-slope form.
We'll use the point \((-2, 4)\) and the slope \(-\frac{3}{4}\). The point-slope form of the line equation is:
\[
y - y_1 = m(x - x_1)
\]
Substituting in the values:
\[
y - 4 = -\frac{3}{4}(x - (-2)) \quad \text{or} \quad y - 4 = -\frac{3}{4}(x + 2)
\]

### 3. Distribute the slope through the parentheses.
Now distribute \(-\frac{3}{4}\):
\[
y - 4 = -\frac{3}{4}x - \frac{3}{4} \cdot 2
\]
Calculating \(-\frac{3}{4} \cdot 2\):
\[
-\frac{3}{4} \cdot 2 = -\frac{6}{4} = -\frac{3}{2}
\]
So we have:
\[
y - 4 = -\frac{3}{4}x - \frac{3}{2}
\]

### 4. Solve for the y-variable.
Now, add \(4\) to both sides:
\[
y = -\frac{3}{4}x - \frac{3}{2} + 4
\]
Convert \(4\) to a fraction with a common denominator:
\[
4 = \frac{8}{2}
\]
Now combine the constants:
\[
y = -\frac{3}{4}x - \frac{3}{2} + \frac{8}{2} = -\frac{3}{4}x + \frac{5}{2}
\]

### Final Output
So, the final equation in slope-intercept form is:
\[
y = -\frac{3}{4}x + \frac{5}{2}
\]