Question

a line passes through the point (3, -7) and has a slope of -7. write an equation in slope-intercept form for this line.

Explanation:

Step1: Recall 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 $m=-7$, so the equation is $y=-7x + b$.

Step2: Substitute the point into the equation

We know that the line passes through the point $(x,y)=(3,-7)$. Substitute $x = 3$ and $y=-7$ into the equation $y=-7x + b$:

$$
LATEXBLOCK0
$$

Step3: Solve for $b$

To solve for $b$, add 21 to both sides of the equation:

$$
LATEXBLOCK1
$$

Step4: Write the final equation

Now that we know $m=-7$ and $b = 14$, substitute these values into the slope - intercept form $y=mx + b$. We get $y=-7x+14$.

Answer:

$y=-7x + 14$