Question

Find the equation of the line that satisfies the given conditions.(Lesson 1.10)

Through$\left(1,7\right)$; slope:$\frac{2}{3}$

Short answer

Equation of the line is $2x-3y+19=0$.

Step-by-step solution

Step 1. Definition of point-slope form.

Point-slope form is the equation of a straight line in the form $y-y_1=m\left(x-x_1\right)$, where m is the slope of the line and$\left(x_1,y_1\right)$ are the coordinates of the given point on the line.

Step 2. Plug the value in equation in general form.

Use the point-slope form to write the equation of the line with $x_1=1$,

$y_1=7$, and the slope is$m=\frac{2}{3}$

$\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-7=\frac{2}{3}\left(x-1\right)\end{array}$

Step 3. Calculate the equation of the line in standard form.

$\begin{array}{l}3\left(y-7\right)=2\left(x-1\right)\\ 3y-21=2x-2\\ 3y-21-2x+2=0\\ -2x+3y-19=0\\ 2x-3y+19=0\end{array}$