Question

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

Through$\left(2,3\right)$; slope: 5

Short answer

Equation of the line is $5x-y-7=0$.

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 slope-intercept form to write the equation of the line with $x_1=2$,

$y_1=3$, and the slope is

$m=5$:

$\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-3=5\left(x-2\right)\end{array}$

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

$\begin{array}{l}y-3=5x-10\\ y-3-5x+10=0\\ -5x+y+7=0\\ 5x-y-7=0\end{array}$