Algebra

Write the equation in slope-intercept form. y–4= 7 8 (x–8)

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Identify the point-slope form given

The equation is already in point-slope form. Our goal is to rewrite it as y = mx + b, which is slope-intercept form.
2

Distribute the slope on the right

Multiply 7/8 by each term inside the parentheses. Distributing removes the parentheses so we can isolate y.
3

Simplify the multiplication

7/8 times 8 equals 7. So the right side simplifies to (7/8)x − 7.
4

Add 4 to both sides

To get y alone, add 4 to both sides of the equation. This moves the −4 from the left side to the right side.
5

Combine constants to finish

−7 + 4 = −3. The equation is now in slope-intercept form y = mx + b, where m = 7/8 and b = −3.

Understanding this problem

Learning Insight

Point-slope form and slope-intercept form both describe the same line — they're just written differently. Converting between them works because you're only using the distributive property and basic algebra. The slope stays the same; only the format changes.

Quick Tip

When the x-value in the parentheses is a multiple of the denominator of the slope, the distribution will always give a whole number — look for that to simplify faster.

Common Mistake

Students often forget to distribute the slope to BOTH terms, writing y − 4 = (7/8)x − 8 instead of (7/8)x − 7. Always multiply the slope by the number inside the parentheses, not just copy it.