Question

question 10
0.5 pts
write the equation of the line that goes through the point (2,-3) and has a slope of -2.

• ( y - 2 = -2(x + 3) )
• ( y - 3 = -2(x + 2) )
• ( y + 3 = -2(x - 2) )
• ( y + 2 = -2(x - 3) )

Explanation:

Step1: Recall point - slope form

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

Step2: Identify $x_1,y_1$ and $m$

We are given the point $(2,-3)$, so $x_1 = 2$ and $y_1=-3$. The slope $m=-2$.

Step3: Substitute into point - slope form

Substitute $x_1 = 2$, $y_1=-3$ and $m = - 2$ into the point - slope form $y - y_1=m(x - x_1)$.
We get $y-(-3)=-2(x - 2)$, which simplifies to $y + 3=-2(x - 2)$.

Answer:

$y + 3=-2(x - 2)$ (corresponding to the option: $y + 3=-2(x - 2)$)