Question

Please help me on this question (7th grade math)

Answer 1

So first we need to take 2 points. Let's use the first two: (2,9) & (3,12)

We know that the equation to find slope is:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

where the subscripts 2 and 1 correspond to either point, the first or the second, either is fine. Let's use (2,9) for the 1 subscripts and (3,12) for the 2 subscripts:

$\frac{12-9}{3-2}=\frac{3}{1}$

So now we now that the slope of this data set is 3. We can now plug it into the equation:

$y=3x+b$

To find the y-intercept for this equation, we need to pick a point and plug it into the equation and solve for b. Let's use (2,9):

$9=3(2)+b$

$9=6+b$

$b=3$

So now we can plug in b and solve for the equation for the data set:

$y=3x+3$

This is the equation that represents the data set that is given and it matches the answer you have circled.