Question

PLSSSSSSSSSSS HELP I HAVE BEEN STUCK ON THIS FOR DAYS

(NO GRAPH JUST THE EQUATION)

Graph the following lines and write the equation in slope-intercept form.


Through the points (5,6) and (−1,4).

(you only need to write the equation y=mx+b for this problem)

Answer 1

y = (1/3)x + 13/3

Explanation:

1. Find the slope (m)

slope = change in y divided by change in x

m=
`(y_(2)-y_(1) )/(x_(2)-x_(1) ) = (6-4)/(5-(-1)) = (2)/(5+1) = (2)/(6) = (1)/(3)`

2. Subsitute 1/3 for m and pick one point to plug into y =mx+b

Ex: (5, 6) -> y= 6 x = 5

6 = 1/3(5) + b

3. Simplify: 6 = 1/3(5) + b

6 = 5/3 + b

4. Solve for b (isolating the variable) by adding 1/3 to both sides

6 - 5/3 = 5/3 - 5/3 + b

5. Simplify: 6 - 5/3 = 5/3 - 5/3 + b

18/3 - 5/3 = b -> 13/3 = b

5. plug in 13/3 for b and 1/3 for m in y = mx + b

y = mx + b -> y = (1/3)x + 13/3

Answer 2

y = 1/3x + 13/3

Explanation:

Slope-Intercept Form: y = mx + b

Slope Formula:
`m=(y_2-y_1)/(x_2-x_1)`

Step 1: Find slope m

`m=(4-6)/(-1-5)`

`m=(-2)/(-6)`

`m=(1)/(3)`

y = 1/3x + b

Step 2: Find y-intercept b

4 = 1/3(-1) + b

4 = -1/3 + b

b = 13/3

Step 3: Write linear equation

y = 1/3x + 13/3