Question

A line goes thought the points (3,5) (6,1)

a. What is the slope of the line? Show your work
b. Write the equation of the line in point-slope form. Show your work.
c. Rewrite the equation into slope-intercept form. Show your work.

Answer 1

Explanation:

Slope = y2 - y1 divided by x2 - x1

Lets make (3,5) as 2, and (6,1) as 1

Slope = 5 - 1 divided by 3 - 6

Slope = -4/3

Point Slope Form: (y - y1) = m(x - x1)

Lets use point (3,5)

(y - 5) = m(x - 3)

m is the slope and we know that the slope is -4/3 so...

(y - 5) = -4/3(x - 3): Point Slope Form Answer

Slope-Intercept Form: y = mx + b

m is the slope and b is the y-intercept

We know that the slope is -4/3

y = -4/3x + b

You can use any of the 2 points and plug it into the equation above to solve for b. So lets use point (3,5)

5 = -4/3(3) + b

5 = -4 + b

b = 9, now plug it back into y = -4/3x + b

y = -4/3x + 9: Slope-Intercept Answer