Question

score: 5/10 penalty: 0.5 off
question
what is the equation of the line that passes through the point (2, -6) and has a slope of -3?
answer attempt 1 out of 2
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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, $x_1 = 2$, $y_1=-6$ and $m=-3$.

Step2: Substitute the values into the formula

Substitute $x_1 = 2$, $y_1=-6$ and $m = - 3$ into the point - slope form:
$y-(-6)=-3(x - 2)$

Step3: Simplify the equation

Simplify the left - hand side: $y + 6=-3(x - 2)$
Expand the right - hand side using the distributive property $a(b - c)=ab-ac$ (here $a=-3$, $b = x$, $c = 2$):
$y+6=-3x+6$
Subtract 6 from both sides of the equation:
$y=-3x+6 - 6$
$y=-3x$
Or we can write it in the standard form $3x + y=0$

Answer:

$y=-3x$ (or $3x + y = 0$)