Question

a line passes through the point (-6, -2) and has a slope of 5/2. 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 are given $m=\frac{5}{2}$ and the point $(x=-6,y = - 2)$.

Step2: Substitute values into the equation

Substitute $x=-6$, $y=-2$ and $m = \frac{5}{2}$ into $y=mx + b$. So, $-2=\frac{5}{2}\times(-6)+b$.

Step3: Solve for $b$

First, calculate $\frac{5}{2}\times(-6)=-15$. Then the equation becomes $-2=-15 + b$. Add 15 to both sides: $b=-2 + 15=13$.

Step4: Write the equation

Now that we have $m=\frac{5}{2}$ and $b = 13$, the equation of the line in slope - intercept form is $y=\frac{5}{2}x+13$.

Answer:

$y=\frac{5}{2}x + 13$