Question

review of writing equations of lines given
the slope a
what is the equation of the line that passes through the point $(-6, -6)$ and has a slope of $\frac{5}{3}$?

1. identify the slope of the line.
2. what is the y-intercept of the line?
3. write the equation of the line in fully simplified slope-intercept form.

Explanation:

1. Identify the slope of the line.

Step1: Recall the given slope.

The problem states the slope of the line is $\frac{5}{3}$.

Step1: Use the slope - intercept form $y = mx + b$.

We know that the slope $m=\frac{5}{3}$, and the line passes through the point $(-6,-6)$. Substitute $x=-6$, $y = - 6$ and $m=\frac{5}{3}$ into the equation $y=mx + b$:
$$-6=\frac{5}{3}\times(-6)+b$$

Step2: Simplify the right - hand side.

$\frac{5}{3}\times(-6)=-10$, so the equation becomes $-6=-10 + b$.

Step3: Solve for $b$.

Add 10 to both sides of the equation: $b=-6 + 10=4$.

Step1: Recall the 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.

Step2: Substitute $m=\frac{5}{3}$ and $b = 4$ into the form.

We get $y=\frac{5}{3}x+4$.

Answer:

$\frac{5}{3}$

2. What is the y - intercept of the line?