Question

seb and mateo discuss the correct linear equation in point - slope form for the table. seb says, the equation should be ( y - 132.8=-35(x + 4)). mateo says, i got something like that, but my equation is ( y+182.2=-35(x - 5)). who is correct, and why?

x	y
-4	132.8
-5	-182.2

• both are correct. the slope is -35 and either ordered pair can be used to fill in for the x - and y - value of the point - slope form.
• neither person is correct. the slope is 35, so the equation should be ( y - 132.8 = 35(x + 4)).
• seb is correct. mateo made the mistake of adding 182.2 to y, when it should have been subtracted.
• mateo is correct. seb made the mistake of subtracting 132.8 from y, when it should have been added.

Explanation:

Step1: Calculate the slope

First, use the two points $(-4, 132.8)$ and $(5, -182.2)$ from the table. The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$.
$$m=\frac{-182.2 - 132.8}{5 - (-4)}=\frac{-315}{9}=-35$$

Step2: Recall point-slope form

The point-slope form of a line is $y - y_1 = m(x - x_1)$, where $(x_1,y_1)$ is a point on the line, and $m$ is the slope.

Step3: Check Seb's equation

Seb uses the point $(-4, 132.8)$: substitute $x_1=-4$, $y_1=132.8$, $m=-35$ into the formula:
$$y - 132.8 = -35(x - (-4)) = -35(x + 4)$$
This is algebraically correct.

Step4: Check Mateo's equation

Mateo uses the point $(5, -182.2)$: substitute $x_1=5$, $y_1=-182.2$, $m=-35$ into the formula:
$$y - (-182.2) = -35(x - 5)$$
$$y + 182.2 = -35(x - 5)$$
This is also algebraically correct.

Answer:

Both are correct. The slope is -35 and either ordered pair can be used to fill in for the x-and y-value of the point slope form.