Question

10. Write the slope-intercept form of the equation for the line.

Answer 1

Explanation:

D is the only answer that has the correct y-intercept of -3/2. The other answers' y-intercepts are on the positive side of the y-axis, but the line does not model that.

Answer:

D) y = -7/8x - 3/2

Answer 2

to get the equation of any straight line, we simply need two points off of it, let's use those from the picture below.

`(\stackrel{x_1}{-4}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-5}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{(-4)}}} \implies \cfrac{-7}{4 +4} \implies \cfrac{ -7 }{ 8 } \implies - \cfrac{ 7 }{ 8 }`

`\begin{array}ll \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}{2}=\stackrel{m}{- \cfrac{ 7 }{ 8 }}(x-\stackrel{x_1}{(-4)}) \implies y -2 = - \cfrac{ 7 }{ 8 } ( x +4) \\\\\\ y-2=- \cfrac{ 7 }{ 8 }x-\cfrac{7}{2}\implies y=- \cfrac{ 7 }{ 8 }x-\cfrac{7}{2}+2\implies {\Large \begin{array}{llll} y=- \cfrac{ 7 }{ 8 }x-\cfrac{3}{2} \end{array}}`