From the given graph, let's find the equation of the red line.
Take two points on the red line:
(-3, 2) and (-4, -1)
Apply the slope intercept form of a linear equation:
y = mx + b
Where m is the slope and b is the y-intercept.
To find the slope, apply the slope formula below:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Where:
(x1, y1) ==> (-3, 2)
(x2, y2) ==> (-4, -1)
Thus, we have:
[tex]\begin{gathered} m=\frac{-1-2}{-4-(-3)} \\ \\ m=\frac{-1-2}{-4+3} \\ \\ m=-\frac{3}{-1} \\ \\ m=3 \end{gathered}[/tex]
The slope(m) of the line is 3
Substitute m for 3 in the slope intercept equation:
y = 3x + b
To find the y-intercept(b), take one point on the line and substitute the values for x and y.
Let's take the point: (-3, 2)
We have:
y = 3x + b
2 = 3(-3) + b
2 = -9 + b
Add 9 to both sides of the equation:
2 + 9 = -9 + 9 + b
11 = b
b = 11
Therefore, the equation of the red line is:
y = 3x + 11
ANSWER:
y = 3x + 11
