Question

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

Answer 1

Answer:

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

Step-by-step 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

Answer 2

Answer:

$\large\boxed{y=-\dfrac{4}{5}x+4}$

Step-by-step explanation:

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

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

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

$m=\dfrac{-4-8}{10-(-5)}=\dfrac{-12}{15}=-\dfrac{12:3}{15:3}=-\dfrac{4}{5}$

Put it to the equation of a line:

$y=-\dfrac{4}{5}x+b$

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

$8=-\dfrac{4}{5\!\!\!\!\diagup_1}(-5\!\!\!\!\diagup^1)+b$

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

$4=b\to b=4$

Finally we have:

$y=-\dfrac{4}{5}x+4$