Question

15 in point - slope form, write the equation of the line if the slope is $\frac{3}{4}$ and the line goes through the point $(2,5)$.

Explanation:

Step1: Recall point - slope formula

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

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

We are given that the slope $m = \frac{3}{4}$ and the point $(x_1,y_1)=(2,5)$.

Step3: Substitute values into the formula

Substitute $m=\frac{3}{4}$, $x_1 = 2$ and $y_1=5$ into the point - slope formula $y - y_1=m(x - x_1)$. We get $y - 5=\frac{3}{4}(x - 2)$.

Answer:

$y - 5=\frac{3}{4}(x - 2)$