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?

Question

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: \[ \boxed{y = \frac{1}{4}x + 2} \]