Question

1. write the equation of the line in fully simplified slope-intercept form.
2. write the equation of the line in fully simplified slope-intercept form.
3. write the equation of the line in fully simplified intercept form.
4. what is the equation of the line that passes through the point (-8, -6) and has a slope of 1?
5. what is the equation of the line that passes through the point (-1, -4) and has a slope of 3?

Explanation:

Problem 6 (Assuming the line in problem 6 has y-intercept -8 and slope -1/2, for example, from the graph)

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.
From the graph, if we can see two points, say $(0,-8)$ (y - intercept) and $(2,-9)$, the slope $m=\frac{-9 - (-8)}{2-0}=\frac{-1}{2}$. And $b=-8$.

Step2: Write the equation

Substitute $m =-\frac{1}{2}$ and $b = - 8$ into $y=mx + b$.
We get $y=-\frac{1}{2}x-8$.

Problem 7 (Assuming the line in problem 7 has y - intercept 4 and slope 1, from the graph)

Step1: Recall slope - intercept form

The slope - intercept form is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept.
From the graph, if we take two points $(0,4)$ (y - intercept) and $(1,5)$, the slope $m=\frac{5 - 4}{1-0}=1$. And $b = 4$.

Step2: Write the equation

Substitute $m = 1$ and $b=4$ into $y=mx + b$.
We get $y=x + 4$.

Problem 8 (Assuming the line in problem 8 has y - intercept - 8 and slope - 1/2, from the graph)

Step1: Recall slope - intercept form

The slope - intercept form is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept.
From the graph, if we take two points $(0,-8)$ (y - intercept) and $(2,-9)$, the slope $m=\frac{-9-(-8)}{2 - 0}=-\frac{1}{2}$. And $b=-8$.

Step2: Write the equation

Substitute $m=-\frac{1}{2}$ and $b = - 8$ into $y=mx + b$.
We get $y=-\frac{1}{2}x-8$.

Problem 9

Answer:

s:

1. $y =-\frac{1}{2}x-8$ (depending on the actual graph, this is an example)
2. $y=x + 4$ (depending on the actual graph, this is an example)
3. $y=-\frac{1}{2}x-8$ (depending on the actual graph, this is an example)
4. $y=x + 2$
5. $y = 3x-1$