Answer:
1) See Attachment.
2) The slope is -2/3.
3) The y-intercept is y=2.
Step-by-step explanation:
We have the two points (6, -2) and (-3, 4) and we know that they are on the same line.
Part 1)
In order to graph a line given two points, we simply need to plot those two points and then draw a line through them.
Please see the attachment.
We would plot (6, -2) and (-3, 4). Then, use a straightedge to connect the two points.
Part 2)
To find the slope, we can use the slope formula.
The slope formula for the slope between any two points is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where (x₁, y₁) and (x₂, y₂) are our two points.
So, let‘s let (6, -2) be (x₁, y₁) And (-3, 4) be (x₂, y₂). Substituting them into the slope formula yields:
[tex]m=\frac{4-(-2)}{-3-6}[/tex]
Evaluate:
[tex]m=\frac{6}{-9}=-2/3[/tex]
So, the slope is -2/3.
We can confirm this using our graph. Remember that the slope measures rise over run.
We are going down by 2 for every 3 to the right.
Part 3)
The y-intercept is where the graph crosses the y-axis.
From the graph, we can see that the graph crosses the y-axis at (0, 2).
Therefore, the y-intercept is y=2.
