Find the y-intercept of the line with equation y − 12 = 4(x − 2).

This equation is written in point-slope form.

In this equation we have the point (2, 12) and the slope of 4.

Slope-intercept form: y = mx + b

m = slope

b = y-intercept

Use the point (2, 12) to solve.

12 = 4(2) + b

12 = 8 + b

12 - 8 = 8 + b - 8

4 = b (y-intercept)

Hope This Helped! Good Luck!

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step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is