Math Problem Statement

Write each equation in slope-intercept form, underline the slope, and circle the y-intercept. The equation is: x + 3y = 0.

Solution

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Task: Write each equation in slope-intercept form, underline the slope, and circle the y-intercept. The equation shown is:

x+3y=0x + 3y = 0

And the instructions state:

  • The slope-intercept form is (7).
  • The slope is (unclear here).
  • The y-intercept is (unclear here).

Let me solve this equation in slope-intercept form for you:

Step 1: Solve the equation x+3y=0x + 3y = 0 for yy.

x+3y=0x + 3y = 0 Subtract xx from both sides: 3y=x3y = -x Now, divide both sides by 3: y=13xy = -\frac{1}{3}x

Step 2: Identify the slope and y-intercept.

  • Slope = 13-\frac{1}{3}
  • y-intercept = 00

Thus, the slope-intercept form is: y=13x+0y = -\frac{1}{3}x + 0

In this form:

  • The slope (underline it) is 13-\frac{1}{3}.
  • The y-intercept (circle it) is 00.

Would you like more details or clarification on this process?

Here are some related questions you might find useful:

  1. How do you find the slope and y-intercept from a linear equation in general?
  2. What does it mean geometrically for the slope to be negative?
  3. How do you graph a line given its slope and y-intercept?
  4. How do you convert a standard form equation (like Ax+By=CAx + By = C) to slope-intercept form?
  5. What are some common mistakes when writing equations in slope-intercept form?

Tip: When converting equations to slope-intercept form, always isolate yy first to easily identify the slope and y-intercept.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope-Intercept Form
Algebra

Formulas

Slope-Intercept Form: y = mx + b

Theorems

Solving Linear Equations
Identifying Slope and y-Intercept

Suitable Grade Level

Grades 7-9