Question

What is the equation in slope-intercept form that passes through the points (-4, 47) and (2, -16)?

Answer 1

y = 10.5x - 37

General Formulas and Concepts:

Pre-Algebra

• Order of Operations: BPEMDAS

Algebra I

Equality Properties

Slope Formula:
`m=(y_2-y_1)/(x_2-x_1)`

Slope-Intercept Form: y = mx + b

• m - slope

• b - y-intercept

Explanation:

Step 1: Define

Point (-4, 47)

Point (2, -16)

Step 2: Find slope m

1. Substitute:
   `m=(-16-47)/(2+4)`
2. Subtract/Add:
   `m=(63)/(6)`
3. Simplify:
   `m=(21)/(2)`

Step 3: Find y-intercept b

1. Define: y = 21/2x + b
2. Substitute: -16 = 21/2(2) + b
3. Multiply: -16 = 21 + b
4. Isolate b: -37 = b
5. Rewrite: b = -37

Step 4: Write linear equation

Combine all parts.

y = 21/2x - 37

y = 10.5x - 37

And we have our final answer!