Question

What is the y-intercept of the line with a slope of − 1/4 that passes through the point (−2, −9/2 )?

Answer 1

`\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-(9)/(2)})~\hspace{10em} slope = m\implies -\cfrac{1}{4} \\\\\\ \begin{array}c \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\left( -\cfrac{9}{2} \right)=-\cfrac{1}{4}[x-(-2)] \\\\\\ y+\cfrac{9}{2}=-\cfrac{1}{4}(x+2)\implies y+\cfrac{9}{2}=-\cfrac{1}{4}x-\cfrac{1}{2}\implies y=-\cfrac{1}{4}x-\cfrac{1}{2}-\cfrac{9}{2}`

`\bf y=-\cfrac{1}{4}x-\cfrac{10}{2}\implies y=-\cfrac{1}{4}x\stackrel{\stackrel{b}{\downarrow }}{\boxed{-5}}\qquad \impliedby \begin{array}ll \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}`

Answer 2

-9/2 = -1/4(-2)+ b

-9/2 = 1/2 + b
Minus 1/2 over

B= -5

Hope this helps!