Question

Find the equation for the linear function that passes through the points ( see photo)

Answer 1

`\large\boxed{y=-(4)/(5)x+4}`

Explanation:

The slope-intercept form of an equation of a line:

`y=mx+b`

m - slope

b - y-intercept

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

We have the points (-5, 8) and (10, -4). Substitute:

`m=(-4-8)/(10-(-5))=(-12)/(15)=-(12:3)/(15:3)=-(4)/(5)`

Put it to the equation of a line:

`y=-(4)/(5)x+b`

Put the coordinates of the point (-5, 8) to the equation, and solveit for b:

`8=-(4)/(5\!\!\!\!\diagup_1)(-5\!\!\!\!\diagup^1)+b`

`8=4+b` subtract 4 from both sides

`4=b\to b=4`

Finally we have:

`y=-(4)/(5)x+4`

Answer 2

f(x) = (-4/5)*x + 4

Explanation:

The line which passes through these points will decrease y by 12 for every x increase of 15. This is the same as decreasing y by 4 for every x increase of 5. This means the slope (rise over run) is -4/5. If this is applied to the first point to find what y is at 0, then the point (0, 4) is on the line.

This means that f(x) = (-4/5)*x + 4