Question

8th grade mathematics| 50 POINTS

The equation y + 6 = 1/3 (x - 9) is written in point-slope form. What is the equation written in slope-intercept form?

A. y = 1/3 x -3
B. y = 1/3 x + 9
C. y = 1/3 x - 9
D. y = 1/3 x + 3

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Answer 1

C. y = 1/3 x - 9

Explanation:

The slope-intercept form is one way to represent a linear function that is set equal to y.

Simplifying and Solving

To find slope-intercept form from point-slope you should simplify the equation and then solve for y.

• y + 6 = 1/3 (x - 9)

Firstly, distribute the 1/3.

• 
  `y+6=(1)/(3)x-3`

Then, subtract the 6 from both sides.

• 
  `y = (1)/(3) x - 9`

This means that the slope-intercept form is y = 1/3 x - 9.

What Slope-Intercept Form Shows

We use slope-intercept form for 2 main reasons; it shows the slope and the y-intercept of a line (hence the name). The formula of slope-intercept is y = mx + b. In this formula, m is the slope and b is the y-intercept.

So, the slope of the line above is 1/3. The y-intercept of the line is -9.