Question

a line passes through the point (-2,5) and has a slope of \frac{1}{4}. write an equation in point - slope form for this line.

Explanation:

Step1: Recall point - slope formula

The point - slope form of a linear equation 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.

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

We are given the point $(-2,5)$, so $x_1=-2$ and $y_1 = 5$. The slope $m=\frac{1}{7}$.

Step3: Substitute values into the formula

Substitute $x_1=-2$, $y_1 = 5$ and $m=\frac{1}{7}$ into the point - slope formula $y - y_1=m(x - x_1)$. We get $y - 5=\frac{1}{7}(x-(-2))$, which simplifies to $y - 5=\frac{1}{7}(x + 2)$.

Answer:

$y - 5=\frac{1}{7}(x + 2)$