Question

1. What is the slope and y-intercept of the linear function?__________

2. Slope:_______

3. y-intercept:_______

5. What is the equation for the function?f(x)=_________

6. Is this function increasing or decreasing?___________

Increase:________

Decrease:_________​

Answer 1

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

`(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{5}-\stackrel{y1}{(-1)}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{(-2)}}} \implies \cfrac{5 +1}{1 +2} \implies \cfrac{ 6 }{ 3 } \implies 2`

`\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}{(-1)}=\stackrel{m}{2}(x-\stackrel{x_1}{(-2)}) \implies y +1 = 2 ( x +2) \\\\\\ y +1 = 2 x +4 \implies {\Large \begin{array}{llll} y = 2 x +3 \end{array}}`