Math Problem Statement

Explain how you can use slope-intercept form to write an equation of a line given its slope and y-intercept.

Solution

The slope-intercept form of a line is written as:

y=mx+by = mx + b

where:

  • mm is the slope of the line.
  • bb is the yy-intercept (the point where the line crosses the yy-axis).

To write the equation of a line given its slope and yy-intercept:

  1. Substitute the slope into the mm position.
  2. Substitute the yy-intercept into the bb position.

The completed sentence in the image would be:

"Substitute the slope for mm and the yy-intercept for bb in the slope-intercept form."

Would you like more details or have any questions about this process?

Here are five related questions that expand on this concept:

  1. How do you determine the slope from two points on a line?
  2. What does the slope represent in a real-world context?
  3. How can you find the yy-intercept if you have a point and the slope?
  4. How do you convert a linear equation from standard form to slope-intercept form?
  5. What is the significance of the sign of the slope in a linear equation?

Tip: To quickly identify the slope and yy-intercept of a line, rearrange the equation into the form y=mx+by = mx + b. The coefficient of xx will be the slope, and the constant term will be the yy-intercept.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

y = mx + b

Theorems

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Suitable Grade Level

Grades 7-9