Question

Find the slope of the line through each pair of points. (1/2, 2/3) and (3/2, 5/3)

Answer 1

slope = 1

to calculate the slope m use the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (
`(1)/(2)`,
`(2)/(3)`) and (x₂, y₂ ) = (
`(3)/(2)`,
`(5)/(3)`)

m = (
`(5)/(3)` -
`(2)/(3)`) / (
`(3)/(2)` -
`(1)/(2)`)

=
`(1)/(1)` = 1

Answer 2

`\bf (\stackrel{x_1}{(1)/(2)}~,~\stackrel{y_1}{(2)/(3)})\qquad (\stackrel{x_2}{(3)/(2)}~,~\stackrel{y_2}{(5)/(3)}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{~~(5)/(3)-(2)/(3)~~}{(3)/(2)-(1)/(2)}\implies \cfrac{~~(3)/(3)~~}{(2)/(2)}\implies \cfrac{1}{1}\implies 1`