Math Problem Statement

Which equation correctly represents the line in slope-intercept form?

Solution

The first image shows a graph of a line with three given points: (8,8)(-8, -8), (0,6)(0, 6), and (8,4)(8, 4).

To determine the correct equation of the line in slope-intercept form, we need to find the slope and the y-intercept.

Step 1: Find the slope (mm)

The formula for the slope between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} Using the points (0,6)(0, 6) and (8,4)(8, 4), we can calculate the slope: m=4680=28=14m = \frac{4 - 6}{8 - 0} = \frac{-2}{8} = -\frac{1}{4}

Step 2: Find the y-intercept (bb)

The general slope-intercept form of a line is: y=mx+by = mx + b We already know the slope m=14m = -\frac{1}{4}, and we can use the point (0,6)(0, 6) (where x=0x = 0) to find bb. Substituting into the equation: 6=14(0)+b6 = -\frac{1}{4}(0) + b b=6b = 6

Step 3: Write the equation

The equation of the line in slope-intercept form is: y=14x+6y = -\frac{1}{4}x + 6

Correct answer:

The correct equation is:
y=14x+6y = -\frac{1}{4}x + 6

This matches the second option in the second image.


Would you like further clarification or any other help? Here are some related questions you might find interesting:

  1. How do you find the slope between two points when they are given in a graph?
  2. What are other forms of linear equations, such as point-slope form and standard form?
  3. How can you find the equation of a line when you are given only one point and the slope?
  4. What is the significance of the y-intercept in a linear equation?
  5. How do you graph a line from its slope-intercept form?

Tip: When solving for the slope, always double-check your calculation to avoid small errors!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope-Intercept Form
Finding Slope and Y-Intercept

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)
Slope-Intercept Form: y = mx + b

Theorems

Equation of a line in slope-intercept form

Suitable Grade Level

Grades 7-9