Linear Function: Match the Graph to its Correct Equation

Question

Which of the following equations corresponds to the function represented in the graph?

00:00 Find the appropriate equation for the function in the graph

00:03 We want to find the slope of the graph

00:07 Let's take 2 points on the graph

00:11 We'll use the formula to find the function's graph slope

00:15 We'll substitute appropriate values according to the given data and solve to find the slope

00:21 This is the slope of the graph

00:26 We'll use the linear equation

00:30 We'll substitute appropriate values and solve to find B

00:41 This is the value of B (intersection point with Y-axis)

00:46 We'll construct the linear equation using the values we found

00:49 And this is the solution to the question

Let's use the below formula in order to find the slope:

$m=\frac{y_2-y_1}{x_2-x_1}$

We begin by inserting the known data from the graph into the formula:

$(0,-2),(-2,0)$

$m=\frac{-2-0}{0-(-2)}=$

$\frac{-2}{0+2}=$

$\frac{-2}{2}=-1$

We then substitute the point and slope into the line equation:

$y=mx+b$

$0=-1\times(-2)+b$

$0=2+b$

Lastly we combine the like terms:

$0+(-2)=b$

$-2=b$

Therefore, the equation will be:

$y=-x-2$

$y=-x-2$