Question

given the slope of -7 and the point (2, 9), which equation is the incorrect representation of the values given? select the correct answer y = -7x + 23 7x + y = 23 y - 9 = -7(x - 2) y = 7x - 9

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line. Given $m=-7$ and $(x_1,y_1)=(2,9)$, the point - slope form is $y - 9=-7(x - 2)$. Let's expand this:
$y-9=-7x + 14$, then $y=-7x+14 + 9=-7x + 23$. So the first and third equations are correct.

Step2: Convert slope - intercept to standard form

Take $y=-7x + 23$, add $7x$ to both sides: $7x + y=23$. So the second equation is correct.

Step3: Check the fourth equation

The fourth equation is $y = 7x-9$, which has a slope of $7$, but our given slope is $-7$. Also, let's check if the point $(2,9)$ lies on it. Substitute $x = 2$: $y=7\times2-9=14 - 9 = 5
eq9$. So this equation is incorrect.

Answer:

D. $y = 7x-9$ (assuming the options are labeled A: $y=-7x + 23$, B: $7x + y=23$, C: $y - 9=-7(x - 2)$, D: $y = 7x-9$)