a line has a slope of -4 and passes through the point (2, -15). write its equation in slope - intercept…

a line has a slope of -4 and passes through the point (2, -15). write its equation in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

a line has a slope of -4 and passes through the point (2, -15). write its equation in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer

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 $m=-4$, so the equation becomes $y=-4x + b$.

Step2: Substitute the point values

Substitute $x = 2$ and $y=-15$ into $y=-4x + b$. We get $-15=-4\times2 + b$.

Step3: Solve for $b$

First, calculate $-4\times2=-8$. Then the equation is $-15=-8 + b$. Add 8 to both sides: $b=-15 + 8=-7$.

Step4: Write the final equation

Substitute $b = - 7$ back into $y=-4x + b$. The equation of the line in slope - intercept form is $y=-4x-7$.

Answer:

$y=-4x - 7$