Question

write the following equation in slope intercept form: y = mx+b
m=-3
(5,-2)

y = -3x - 13
y = -3x - 17
y = -3x + 17
y = -3x + 13

Explanation:

Step1: Recall slope-intercept formula

Slope - intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We know that \(m=- 3\) and the line passes through the point \((x,y)=(5,-2)\).

Step2: Substitute values into the formula

Substitute \(m = - 3\), \(x = 5\) and \(y=-2\) into \(y=mx + b\). We get \(-2=-3\times5 + b\).

Step3: Solve for \(b\)

First, calculate \(-3\times5=-15\). So the equation becomes \(-2=-15 + b\). Then, add 15 to both sides of the equation: \(b=-2 + 15=13\).

Step4: Write the equation

Now that we know \(m=-3\) and \(b = 13\), the equation in slope - intercept form is \(y=-3x + 13\).

Answer:

\(y=-3x + 13\) (the option: \(y = - 3x+13\))