Math Problem Statement

n the equation y=−2/3 x+2, the slope is −2/3​ and the y-intercept is 2.

1 point

TRUE

FALSE

Solution

The statement is TRUE.

In the equation y=23x+2y = -\frac{2}{3}x + 2, the slope-intercept form of a line is used, which is given by:

y=mx+by = mx + b

where mm is the slope and bb is the y-intercept. In this equation:

  • The slope mm is 23-\frac{2}{3}.
  • The y-intercept bb is 22.

Since both the slope and y-intercept are correctly identified, the statement is true.

Would you like more details or have any further questions? Here are 5 related questions to deepen your understanding:

  1. How do you find the slope of a line from two points?
  2. How do you convert a linear equation from standard form to slope-intercept form?
  3. What does the slope of a line tell you about the direction of the line?
  4. How do you graph a line given its slope and y-intercept?
  5. What happens to the graph of a line if the y-intercept is negative?

Tip: In the slope-intercept form y=mx+by = mx + b, the value of mm determines how steep the line is, and bb tells you where the line crosses the y-axis.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

Slope-intercept form y = mx + b

Theorems

Slope-intercept theorem

Suitable Grade Level

Grades 6-8