Question

The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y – 4 = y minus 4 equals StartFraction one-fourth EndFraction left-parenthesis x minus 9 right-parenthesis.(x – 8). What is the slope-intercept form of the equation for this line?

y = y equals StartFraction one-fourth EndFraction x minus 12.x – 12
y = y equals StartFraction one-fourth EndFraction x minus 4.x – 4
y = y equals StartFraction one-fourth EndFraction x plus 2.x + 2
y = y equals StartFraction one-fourth EndFraction x plus 6.x + 6

Answer 1

To find the correct slope-intercept form of the equation of the line given the points (8, 4) and (0, 2), we can follow these steps:

1. **Calculate the slope (m)**: The slope \( m \) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
For points (8, 4) and (0, 2):
\[
m = \frac{2 - 4}{0 - 8} = \frac{-2}{-8} = \frac{1}{4}
\]

2. **Use point-slope form to write the equation**: We can use the point-slope form of the equation of a line, which is:
\[
y - y_1 = m(x - x_1)
\]
Using the point (8, 4):
\[
y - 4 = \frac{1}{4}(x - 8)
\]

3. **Convert to slope-intercept form (y = mx + b)**: Distributing on the right side:
\[
y - 4 = \frac{1}{4}x - 2
\]
Adding 4 to both sides:
\[
y = \frac{1}{4}x - 2 + 4
\]
\[
y = \frac{1}{4}x + 2
\]

Now, we can find the correct slope-intercept form from the options given:

- **Correct answer**:
\[
y = \frac{1}{4}x + 2
\]

So, the slope-intercept form of the equation for this line is:
\[
\boxed{y = \frac{1}{4}x + 2}
\]