Question

A linear function has the same y-intercept as x + 4y = 20 and its graph contains the point (3, 6). Find the slope of the linear function.

Answer 1

1/3 is the slope.

Explanation:

First, we need to find the y-intercept of x + 4y = 20.

x + 4y = 20

Subtract x from both sides.

4y = -x + 20

Divide both sides by 4.

y = -1/4x + 5

Input 0 as x to find the y-intercept.

y = -1/4(0) + 5

Simplify.

y = 5

Now we know the y-intercept is (0,5). Now we need to include to find a slope that contains (0,5) and (3,6). We can use the slope formula:

`(y_(2)-y_(1))/(x_(2)-x_1)}`

(5 - 6)/(0 - 3) = m

-1/-3 = m

Simplify.

1/3 = m

1/3 is the slope.