Question

2 multiple choice 10 points what is the equation of the line that goes through the points (-2, 4) and has a slope of -\frac{1}{2}? \bigcirc y = -\frac{1}{2}x + 3 \bigcirc y = -2x + 3 \bigcirc y = -\frac{1}{2}x - 3 \bigcirc y = \frac{1}{2}x + 3

Explanation:

Step1: 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 of the line.
Here, $x_1=-2$, $y_1 = 4$ and $m=-\frac{1}{2}$.

Step2: Substitute values into point - slope form

Substitute the values into the formula: $y - 4=-\frac{1}{2}(x - (-2))$.
Simplify the right - hand side: $y - 4=-\frac{1}{2}(x + 2)$.

Step3: Distribute and solve for y

Distribute $-\frac{1}{2}$ on the right - hand side: $y - 4=-\frac{1}{2}x-1$.
Add 4 to both sides of the equation: $y=-\frac{1}{2}x-1 + 4$.
Simplify the constant terms: $y=-\frac{1}{2}x+3$.

Answer:

$y = -\frac{1}{2}x + 3$ (the first option)