Question

which equation of a line has a slope of -3 and passes through point (2, 4)?
y = -3x - 10
y = -3x + 10
y = 3x + 10
y = 3x - 10

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. Here, $m=-3$, $x_1 = 2$, and $y_1=4$.

Step2: Substitute values into point - slope form

Substitute the values into the formula: $y - 4=-3(x - 2)$.

Step3: Simplify the equation

First, distribute the - 3 on the right - hand side: $y - 4=-3x+6$. Then, add 4 to both sides of the equation: $y=-3x + 6+4$, which simplifies to $y=-3x + 10$.

Answer:

B. $y = - 3x+10$