Math Problem Statement

Write the equation of the linear function below in slope-intercept form.

Solution

Let's analyze the linear graph in your image to write its equation in slope-intercept form y=mx+by = mx + b, where:

  • mm is the slope.
  • bb is the y-intercept.

Step 1: Identify the y-intercept bb

The graph intersects the y-axis at y=1y = 1, which means:

  • b=1b = 1.

Step 2: Find the slope mm

The slope is defined as: m=riserunm = \frac{{\text{rise}}}{{\text{run}}} From the graph:

  • Choose two points the line passes through: (0,1)(0, 1) and (2,2)(2, -2).
  • Rise: 21=3-2 - 1 = -3
  • Run: 20=22 - 0 = 2

So, the slope is: m=32m = \frac{-3}{2}

Step 3: Write the equation in slope-intercept form

Now that we know the slope m=32m = -\frac{3}{2} and the y-intercept b=1b = 1, the equation becomes: y=32x+1y = -\frac{3}{2}x + 1

This is the equation of the line in slope-intercept form.


Do you have further questions or need additional details?


Here are 5 follow-up questions you may find useful:

  1. How do you calculate the slope if only given two points?
  2. What happens to the equation if the slope is positive?
  3. How do you find the equation if the y-intercept is not given?
  4. Can we express this equation in standard form?
  5. What are other forms of linear equations besides slope-intercept?

Tip: When calculating slope, be careful with signs to avoid mistakes!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

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

Theorems

Slope formula

Suitable Grade Level

Grades 8-10