The slope of a line often referred to as the ([tex]\frac{rise}{run}[/tex]) is the rate of change in a line. It can be found using the following formula.
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) are points on the line. For each problem, substitute the points on the line into the formula and solve for the slope.
1. [tex]\frac{1}{2}[/tex]
(0, 2), (-2, 1)
[tex]=\frac{1-2}{-2-0}\\\\=\frac{-1}{-2}\\\\=\frac{1}{2}[/tex]
2. 2
(-2, -1), (0, 3)
[tex]=\frac{3-(-1)}{0-(-2)}\\\\=\frac{3+1}{0+2}\\\\=\frac{4}{2}\\\\=2[/tex]
3. 4
(1, 0), (2, 4)
[tex]=\frac{4-0}{2-1}\\\\=\frac{4}{1}\\\\=4[/tex]
4. 1
(6, 2), (2, -2)
[tex]=\frac{-2-2}{2-6}\\\\=\frac{-4}{-4}\\\\=1[/tex]
5.[tex]\frac{3}{5}[/tex]
(-1, 1), (4, 4)
[tex]=\frac{4-1}{4-(-1)}\\\\=\frac{3}{4+1}\\\\=\frac{3}{5}[/tex]
6. [tex]\frac{1}{3}[/tex]
(-7, 4), (2, 1)
[tex]=\frac{4 -1}{2-(-7)}\\\\=\frac{3}{2+7}\\\\=\frac{3}{9}\\\\=\frac{1}{3}[/tex]
7. 0
(5, -3), (-2, -3)
[tex]=\frac{-3-(-3)}{-2-5}\\\\=\frac{-3+3}{-7}\\\\=0[/tex]
8. [tex]\frac{7}{5}[/tex]
(-3, 2), (2, 7)
[tex]=\frac{7-2}{2 - (-3)}\\\\=\frac{7}{2+3}\\\\=\frac{7}{5}[/tex]
9. 8
(2, 16), (3, 24)
[tex]=\frac{24-16}{3-2}\\\\=\frac{8}{1}\\\\=8[/tex]
