Question

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

Answer 1

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

Answer 2

slope = 1

to calculate the slope m use the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = ($\frac{1}{2}$,$\frac{2}{3}$) and (x₂, y₂ ) = ($\frac{3}{2}$,$\frac{5}{3}$)

m = ($\frac{5}{3}$ - $\frac{2}{3}$) / ($\frac{3}{2}$ - $\frac{1}{2}$)

= $\frac{1}{1}$ = 1