Question

A line has a slope of -1 and contains the points (1, 2) and (2, y). The value of y is

Answer 1

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

Answer 2

y = 1

calculate the slope m using the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, 2 ) and (x₂, y₂ ) = (2, y )

m = $\frac{y-2}{2-1}$ = y - 2

now m = -1, hence

y - 2 = -1 ( add 2 to both sides )

y = 1