So, the slope is in fact a change in y divided by a change in x:
[tex]m=\frac{\Delta y}{\Delta x}[/tex]
To get this change, we can choose two points in the line.
In this case, we can pick the points marked, (0, -5) and (3, -1).
The change in y will be the difference between the y values. It is important to use the points in the same order to calculate the change in y and in x. so let's denote:
Point 1 - (0, -5)
Point 2 - (3, -1)
Let's see the difference from Point 1 to Point 2:
[tex]\begin{gathered} \Delta y=y_2-y_1=-1-(-5)=-1+5=4 \\ \Delta x=x_2-x_1=3-0=3 \end{gathered}[/tex]
So, the slope is:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{4}{3}[/tex]
The y-intercept is the y-value in which the line intersects the y-axis, the vertical one. We can see that this happens at exaclty the point (0, -5), so the y-intercept is y = -5.
The line equation in the slope-intercept form is:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept. We already saw that:
[tex]\begin{gathered} m=\frac{4}{3} \\ b=-5 \end{gathered}[/tex]
So, the equation is:
[tex]y=\frac{4}{3}x-5[/tex]
