5. the graph of a linear relationship has a slope of -5 and passes through the point (2, -12). write the…

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 are given that $m=-5$. So the equation becomes $y=-5x + b$.

Step2: Substitute the point into the equation

We know the line passes through the point $(2,-12)$. Substitute $x = 2$ and $y=-12$ into $y=-5x + b$. So, $-12=-5\times2 + b$.

Step3: Solve for $b$

First, calculate $-5\times2=-10$. Then the equation $-12=-10 + b$ can be solved for $b$ by adding 10 to both sides. We get $b=-12 + 10=-2$.

Step4: Write the final equation

Substitute $b = - 2$ back into $y=-5x + b$. The equation of the line is $y=-5x-2$.

Answer:

$y=-5x - 2$