Question

WILL PAY 40 POINTS AND BRAINLIEST!!!!

Answer 1

Answer:

Part A)

The slope is 3.

Part B)

$\displaystyle y-1=3(x+3)$

Part C)

$\displaystyle y=3x+10$

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:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

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:

$\displaystyle m=\frac{4-1}{-2-(-3)}$

Evaluate:

$\displaystyle m=\frac{3}{-2+3}=\frac{3}{1}=3$

Hence, the slope of our line is 3.

Part B)

Point-slope form is given by:

$\displaystyle y-y_1=m(x-x_1)$

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:

$\displaystyle y-1=3(x-(-3))$

Simplify. Hence, our point-slope form is:

$\displaystyle y-1=3(x+3)$

Part C)

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

$\displaystyle y-1=3(x+3)$

Distribute on the right:

$\displaystyle y-1=3x+9$

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

$\displaystyle y=3x+10$