Question

Intercept from a table

Answer 1

$\bf \begin{array}{ccll} x&y\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \boxed{14}&\boxed{-5}\\ 21&-3\\ \boxed{28}&\boxed{-1} \end{array}\impliedby \textit{we'll use two points to get the slope}$

$\bf (\stackrel{x_1}{14}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{28}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-(-5)}{28-14}\implies \cfrac{-1+5}{28-14} \\\\\\ \cfrac{4}{14}\implies \cfrac{2}{7} \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-5)=\cfrac{2}{7}(x-14) \\\\\\ y+5=\cfrac{2}{7}x-4$

now, to get the y-intercept, we simply set x = 0 and solve for y, and to get the x-intercept, we set y = 0 and solve for x.

$\bf \stackrel{\textit{y-intercept, x = 0}}{y+5=\cfrac{2}{7}(0)-4}\implies y+5=-4\implies y=-9\qquad \qquad \stackrel{y-intercept}{(0~,-9)}\\\\ -------------------------------\\\\ \stackrel{\textit{x-intercept, y = 0}}{(0)+5=\cfrac{2}{7}x-4}\implies 5=\cfrac{2x}{7}-4\implies 9=\cfrac{2x}{7}\implies 63=2x \\\\\\ \cfrac{63}{2}=x\implies 31\frac{1}{2}=x\qquad \qquad \qquad \qquad \qquad \qquad \qquad \stackrel{x-intercept}{\left( 31\frac{1}{2}~,~0 \right)}$