Answer:
\(y=\frac{4}{3}x+4\)
Step-by-step explanation:
The general form of the slope-intercept equation is:
\(y = mx + b\)
where \(m\) is the slope of the line, and \(b\) is the intercept (the point at which the line crosses the y-axis).
In this case we can see by the graph that the intercept is at 4, so \(b = 4\).
And to find the slope, we need to find two points \((x_{1}, y_{1})\) and \((x_{2}, y_{2})\) of the graph, I will take the points \((-3,0)\) and \((0,4)\), so:
\(x_{1}=-3\\y_{1}=0\\x_{2}=0\\y_{2}=4\\\)
And with this data we calculate the slope as follows:
\(m=\frac{y_{2}-y_{1}}{x_{2}-x_{2}}\)
\(m=\frac{4-0}{0-(-3)}\)
\(m=\frac{4}{3}\)
And finally, we substitute the values of \(m\) and \(b\) in the slope-intercept equation:
\(y = mx + b\)
\(y=\frac{4}{3}x+4\)
