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]

Lines k and I are parallel and cut by transversal j.


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A.<6 and <7 are complementary

B. <4 and <8 form a linear pair

C. <1 and <2 are congruent

D.
<2 and <7 form vertical angles

standard covert 3x-24 = 1 ​

URGENTTTTTTT
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