Match the Function Equation: Analyzing X-Y Values from -3 to 5

Question

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

00:00 Find the function equations according to the given table

00:03 We'll use the formula for finding the graph slope

00:09 We'll substitute appropriate values according to the data and solve for the slope

00:19 Negative times negative is always positive, so we'll multiply

00:24 This is the graph slope

00:32 We'll use the line equation to find intersection point B

00:39 We'll substitute appropriate values according to the data and solve for B

00:48 We'll isolate B

00:55 This is intersection point B

00:59 Now we'll substitute appropriate values in the line equation to find the equation

01:03 And this is the solution to the question

We will begin by using the formula for finding slope:

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

First let's take the points:

$(-1,4),(3,8)$

$m=\frac{8-4}{3-(-1)}=$

$\frac{8-4}{3+1}=$

$\frac{4}{4}=1$

Next we'll substitute the point and slope into the line equation:

$y=mx+b$

$8=1\times3+b$

$8=3+b$

Lastly we'll combine like terms:

$8-3=b$

$5=b$

Therefore, the equation will be:

$y=x+5$

$y=x+5$