Question

What is the equation of the red line graphed below?

Answer 1

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:

`m=(y2-y1)/(x2-x1)`

Where:

(x1, y1) ==> (-3, 2)

(x2, y2) ==> (-4, -1)

Thus, we have:

`\begin{gathered} m=(-1-2)/(-4-(-3)) \\ \\ m=(-1-2)/(-4+3) \\ \\ m=-(3)/(-1) \\ \\ m=3 \end{gathered}`

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