Question

3.3.3 quiz: point - slope equation of a line
find a point - slope equation of the line.
a. $y - 9 = 2(x - 1)$
b. $y - 9 = -2(x - 1)$
c. $y + 9 = -2(x + 1)$
d. $y + 9 = 2(x + 1)$

Explanation:

Step1: Recall Point - Slope Formula

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. We know the point $(x_1,y_1)=(1,9)$. Now we need to find the slope $m$.

Step2: Analyze the Slope

Looking at the line, as $x$ increases by 1 (from $x = 1$), $y$ increases by 2 (since the line is rising). So the slope $m=\frac{\text{change in }y}{\text{change in }x}=2$.

Step3: Substitute into Point - Slope Formula

Substitute $x_1 = 1$, $y_1=9$ and $m = 2$ into the point - slope formula $y - y_1=m(x - x_1)$. We get $y - 9=2(x - 1)$.

Answer:

A. $y - 9 = 2(x - 1)$