Question

question
what is the equation of the line that passes through the point (4, -4) and has a slope of -3?

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation is given by $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.
Here, $x_1 = 4$, $y_1=-4$ and $m=-3$.

Step2: Substitute values into point - slope form

Substitute $x_1 = 4$, $y_1=-4$ and $m=-3$ into the point - slope formula:
$y-(-4)=-3(x - 4)$

Step3: Simplify the equation

Simplify the left - hand side: $y + 4=-3(x - 4)$
Expand the right - hand side using the distributive property $a(b - c)=ab-ac$ (here $a=-3$, $b = x$, $c = 4$):
$y+4=-3x+12$
Subtract 4 from both sides to get the slope - intercept form ($y=mx + b$):
$y=-3x+12 - 4$
$y=-3x + 8$

We can also write it in the standard form $Ax+By = C$ (where $A$, $B$, $C$ are integers and $A\geq0$).
Starting from $y=-3x + 8$, add $3x$ to both sides:
$3x+y=8$

Answer:

The equation of the line in slope - intercept form is $y=-3x + 8$ (or in standard form $3x + y=8$)