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

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

Answer Link

gmany gmany · Answer 2 · 2019-07-06T21:06:33+02:00

Answer:

[tex]\large\boxed{y=-\dfrac{4}{5}x+4}[/tex]

Step-by-step explanation:

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

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

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

[tex]m=\dfrac{-4-8}{10-(-5)}=\dfrac{-12}{15}=-\dfrac{12:3}{15:3}=-\dfrac{4}{5}[/tex]

Put it to the equation of a line:

[tex]y=-\dfrac{4}{5}x+b[/tex]

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

[tex]8=-\dfrac{4}{5\!\!\!\!\diagup_1}(-5\!\!\!\!\diagup^1)+b[/tex]

[tex]8=4+b[/tex] subtract 4 from both sides

[tex]4=b\to b=4[/tex]

Finally we have:

[tex]y=-\dfrac{4}{5}x+4[/tex]