Question

Determine the intercepts of the line that passes through the following points.

Answer 1

Slope-intercept form: y = mx + b (m is the slope, b is the y-intercept or the y value when x = 0 -- > (0 , y))

To find the slope (m), you use the slope formula and plug in 2 points.

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

(x₁ , y₁) = (1 , 20)

(x₂, y₂) = (5 , 10)

$m=\frac{10-20}{5-1}=\frac{-10}{4}=-\frac{5}{2}$

$y=-\frac{5}{2}x+b$    To find b, plug in a point into the equation (1,20)

$20=-\frac{5}{2}(1)+b$    Add 5/2 on both sides

$20+\frac{5}{2}=b$

$\frac{40}{2}+\frac{5}{2}=b$

22.5 = b

$y=-\frac{5}{2}x+22.5$

Your y-intercept is (0, 22.5) or (0, 45/2)

The x-intercept is the x value when y = 0 ---> (x, 0)

To find the x-intercept, set y = 0 in the equation

0 = -5/2x + 22.5

-22.5 = -5/2x     Multiply -2/5 on both sides to get x by itself

9 = x

Your x-intercept is (9, 0)