Question

Part C
What is the equation represented by the graph?

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}{1}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{24}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{24}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{ 16 }{ 2 } \implies 8`

`\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-\stackrel{y_1}{8}=\stackrel{m}{ 8}(x-\stackrel{x_1}{1}) \\\\\\ y-8=8x-8\implies {\Large \begin{array}{llll} y=8x \end{array}}`

Answer 2

`y=8x`

Explanation:

We can see that this line has a constant of proportionality. That is — x is proportional to y and vice versa. This means that the equation for the line's equation will be in the form:

`y = mx`

where
`m` is the ratio of x to y.

This ratio is also known as the line's slope. We can solve for the slope using the equation:

slope = rise / run

slope =
`\Delta`y /
`\Delta`x

slope = 8 / 1

slope = 8

`m=8`

So, the equation of the line is:

`y=mx`

`\boxed{y=8x}`