Answer:
y = 8x
Step-by-step explanation:
The slope-intercept form of a linear equation is:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Slope-intercept form of a linear equation}}\\\\\large\text{$y=mx+b$}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\;\textsf{$m$ is the slope.}\\\phantom{ww}\bullet\;\;\textsf{$b$ is the $y$-intercept.}\\\end{array}}[/tex]
To find the slope (m) of the graphed line, we can substitute two points on the line into the slope formula. Let's use points (0, 0) and (2, 16):
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{16-0}{2-0}=\dfrac{16}{2}=8[/tex]
Therefore, the slope of the line is 8.
The y-intercept is the point at which the line crosses the y-axis.
In this case, the line crosses the y-axis at the origin (0, 0), so b = 0.
Substitute m = 8 and b = 0 into the slope-intercept formula:
[tex]y=8x+0\\\\y=8x[/tex]
Therefore, the equation of the graphed line in slope-intercept form is:
[tex]\LARGE\boxed{\boxed{y=8x}}[/tex]
