Plz explain this clearly to me, i'm struggling

They give you a table values that show different points on a line. Using these points they want you to figure out an equation for the line and use that to find the intercepts.

Now, to write this equation we first must look for the slope. Slope is the change in y (rise) over the change in x (run).

Looking at the chart we see x increases by 3 and that y decreases by 6 each time. When putting rise over run, we would make six negative because it's going down.

-6/3 = -2. so that's our slope. we will use this to setup out equation in slope intercept form.

slope intercept follows the format of y = mx + b. where m is the slope and b is the y intercept.

when we look for the y intercept, we are really solving for b. So in our equation y = -2x + b, we can solve this by taking a point from the line given in the table and insert it in. such as (8,2).

We would put: 2 = -2(8) + b
2 = -16 + b
18 = b. so our y int is (0, 18) x is zero because anypoint on the y axis has 0 x.

to find our x int, we set y to 0. so we get:
0 = -2x + 18
-18 = -2x
x = 9

so our x int is (9,0) y is zero because anypoint in the x axis has a y of 0.