Question

A y = 1/2x + 5 B y = 1/2x + 7 c y = 2x + 5 D y = y = 2x + 7

Answer 1

`\Large \boxed{{y=-(2)/(3)x +12}}`

Explanation:

y = mx + b (slope-intercept form of a line)

m is slope

b is y-intercept

The y-intercept of the line is (0, 12) or 12.

y = mx + 12

The slope of the line can be found through rise over run.

(0, 12) and (18, 0) are two points on the line.

m = (y2-y1)/(x2-x1)

m = (0-12)/(18-0)

m = -12/18

m = -2/3

The slope of the line is -2/3.

y = -2/3x + 12

Answer 2

`y=-(2)/(3)x+12`

Explanation:

Step 1: Rule out answers

The answer cannot be B or D because the y-intercept is at 12(b = 12) and in a linear equation y=mx+b, b is the y intercept.

B has the y intercept at 18

D has the y intercept at 18

Step 2: Find the slope

The slop is the change in y over the change in x. We can also write this as
`(rise)/(run)`

We see it lowers by 2 so we will put -2 as the numerator

We also the x value increase by 3 every time it gets lowered by 2 so the run is 3

Therefore the slope is
`-(2)/(3)`

Step 3: Plug in the the variables to get the linear equation

`y=mx+b`

`y=-(2)/(3)x+12`

Therefore the answer is A.
`y=-(2)/(3)x+12`