Question

a line passes through the point (4, 5) and has a slope of -2. write an equation in point - slope form for this line.

Explanation:

Step1: Recall point - slope formula

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 values of $x_1,y_1$ and $m$

We are given that the line passes through the point $(4,5)$, so $x_1 = 4$ and $y_1=5$. The slope $m=-2$.

Step3: Substitute values into the formula

Substitute $x_1 = 4$, $y_1 = 5$ and $m=-2$ into the point - slope formula $y - y_1=m(x - x_1)$. We get $y - 5=-2(x - 4)$.

Answer:

$y - 5=-2(x - 4)$