WILL PAY 40 POINTS AND BRAINLIEST!!!!
A line goes through the points (-3 1) and (-2 4)
(a) What is the slope of the line? Show your work.
(b) Write the equation of the line in point-slope form. Show your work.
(c) Write the equation of the line in slope-intercept form. Show your work.

Answer:

Part A)

The slope is 3.

Part B)

[tex]\displaystyle y-1=3(x+3)[/tex]

Part C)

[tex]\displaystyle y=3x+10[/tex]

Step-by-step explanation:

We know that the line goes through the points (-3, 1) and (-2, 4).

Part A)

To find the slope of a line given two points, we can use the slope formula:

[tex]\displaystyle 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 (-3, 1) be (x₁, y₁) and let (-2, 4) be (x₂, y₂). Substitute appropriately:

[tex]\displaystyle m=\frac{4-1}{-2-(-3)}[/tex]

Evaluate:

[tex]\displaystyle m=\frac{3}{-2+3}=\frac{3}{1}=3[/tex]

Hence, the slope of our line is 3.

Part B)

Point-slope form is given by:

[tex]\displaystyle y-y_1=m(x-x_1)[/tex]

Where m is our slope and (x₁, y₁) is a point.

So, let’s substitute 3 for m.

For our point, we can use either of the two given. Let’s use (-3, 1) for consistency. So, let (-3, 1) be (x₁, y₁). Therefore:

[tex]\displaystyle y-1=3(x-(-3))[/tex]

Simplify. Hence, our point-slope form is:

[tex]\displaystyle y-1=3(x+3)[/tex]

Part C)

To rewrite into slope-intercept form, we can just solve for y from our point-slope form. So, we have:

[tex]\displaystyle y-1=3(x+3)[/tex]

Distribute on the right:

[tex]\displaystyle y-1=3x+9[/tex]

Add 1 to boths sides. So, our slope-intercept equation is:

[tex]\displaystyle y=3x+10[/tex]

Wilscy owns a toy store. The number of toy trains sold (in thousands) from 2000 through 2005 can be modeled by M(x) = −0.5x3 + 2x2 − x + 9. The average cost per toy train (in dollars) can be modeled by N(x) = 0.3x + 7, where x represents the number of years since 2000. The total revenue Wilscy made by the sale of toy trains is the product of the number of toy trains sold and the average cost per toy train. Identify a polynomial P(x) that can be used to model the total revenue.

Options:
a: P(x) = −0.15x4 − 2.9x3 + 13.7x2 − 4.3x + 63
b: P(x) = −0.5x3 + 2x2 − 0.7x + 2
c: P(x) = −0.15x4 + 4.1x3 + 14.3x2 − 9.7x + 63
d: P(x) = −0.5x3 + 2x2 − 1.3x + 16

What is the y-value of point A?

Round your answer to the nearest tenth of a degree.

Graph this line using the slope and y-intercept:
y = 8x - 6
Click to select points on the graph.
8
6
4
No
-6
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-10
-8
0
co
4
2
6
10
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CO
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