Question

What is the y-intercept of a line that has a slope of 3 and passes through point (-1, -7)?

–10

–4

3

7

Answer 1

we can do so by getting the equation of the line, let's use the slope and point given

`(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{ 3}(x-\stackrel{x_1}{(-1)}) \implies y +7 = 3 ( x +1)`

`y+7=3x+3\implies y=3x \stackrel{ \stackrel{\textit{\LARGE b}}{\downarrow } }{-4}\qquad \impliedby \qquad \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}`