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.
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
(x₁ , y₁) = (1 , 20)
(x₂, y₂) = (5 , 10)
[tex]m=\frac{10-20}{5-1}=\frac{-10}{4}=-\frac{5}{2}[/tex]
[tex]y=-\frac{5}{2}x+b[/tex] To find b, plug in a point into the equation (1,20)
[tex]20=-\frac{5}{2}(1)+b[/tex] Add 5/2 on both sides
[tex]20+\frac{5}{2}=b[/tex]
[tex]\frac{40}{2}+\frac{5}{2}=b[/tex]
22.5 = b
[tex]y=-\frac{5}{2}x+22.5[/tex]
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)
