Question

a line has a slope of -2 and passes through the point (-3, 6). write its equation in slope - intercept form.
name two different ways to graph a line, graph the line, and then write the equation in standard form.

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know that the slope $m=-2$.

Step2: Substitute the point and slope into the equation

We know the line passes through the point $(-2,6)$ and $m = - 2$. Substitute $x=-2$, $y = 6$ and $m=-2$ into $y=mx + b$:
\[6=-2\times(-2)+b\]

Step3: Solve for $b$

First, calculate $-2\times(-2)=4$. Then the equation becomes $6 = 4 + b$. Subtract 4 from both sides: $b=6 - 4=2$.

Step4: Write the equation

Now that we know $m=-2$ and $b = 2$, substitute these values into the slope - intercept form $y=mx + b$.

Answer:

$y=-2x + 2$