Question

Find the equation of the line that satisfies the given conditions.

Through $\left(-2,4\right)$; slope: $-1$

Short answer

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

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. Write the equation in general form.

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

$y_1=4$, and the slope is $m=-1$:

$\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-4=-1\left(x-\left(-2\right)\right)\end{array}$

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

$\begin{array}{l}y-4=-1\left(x+2\right)\\ y-4=-x-2\\ y-4+x+2=0\\ x+y-2=0\end{array}$