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