Question

The point-slope form of a line that has a slope of One-fourth and passes through the point (3, 0) is shown.

y minus 0 = one-fourth (X minus 3)

What is the equation in slope-intercept form?
y = one-fourth x minus 3
y = one-fourth x minus three-fourths
y = three-fourths x minus one-fourth
y = one-fourth x minus StartFraction 1 Over 12 EndFraction

Answer 1

To convert the point-slope form of the line \( y - 0 = \frac{1}{4}(x - 3) \) into slope-intercept form (which is \( y = mx + b \)), we can follow these steps:

1. Start with the equation in point-slope form:
\[
y = \frac{1}{4}(x - 3)
\]

2. Distribute \(\frac{1}{4}\):
\[
y = \frac{1}{4}x - \frac{1}{4} \cdot 3
\]

3. Calculate \(-\frac{1}{4} \cdot 3\):
\[
y = \frac{1}{4}x - \frac{3}{4}
\]

Now, we have the equation in slope-intercept form:
\[
y = \frac{1}{4}x - \frac{3}{4}
\]

Thus, the correct option is:
**y = one-fourth x minus three-fourths.**