Question

Find the equation of the linear function represented by the table below in slope-

intercept form.
X
0
1
2
3
4

Y
-7
0
7
14
21

Answer 1

f(x) = 7x - 7

or

y = 7x - 7

Explanation:

The y intercept is the point (0, -7), so the y intercept is -7. The slope is the change in y over the change in x. y is increasing by 7 as x is increasing by 1, so the slope is 7/1 or just 7

y = mx + b put the slope in for m and the y-intercept for b

y = 7x - 7

Helping in the name of Jesus.

Answer 2

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}{7})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{21}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{21}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{2}}} \implies \cfrac{ 14 }{ 2 } \implies 7`

`\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}{ 7}(x-\stackrel{x_1}{2}) \\\\\\ y-7=7x-14\implies {\Large \begin{array}{llll} y=7x-7 \end{array}}`