Math Problem Statement

The equation of a line is y = 3 - 5x. What is the y-intercept of the line?

Solution

The equation of the line given is y=35xy = 3 - 5x.

The yy-intercept of a line is the value of yy when x=0x = 0. To find it:

  1. Substitute x=0x = 0 into the equation: y=35(0)y = 3 - 5(0)

  2. Simplify: y=3y = 3

Thus, the yy-intercept of the line is 3.

Would you like further clarification or additional examples? Here are five related questions for further exploration:

  1. What is the slope of this line, and how is it interpreted geometrically?
  2. How can the equation be rewritten in standard form Ax+By=CAx + By = C?
  3. What is the x-intercept of this line, and how is it calculated?
  4. How would the graph of this line change if the slope were doubled?
  5. How do you determine the equation of a line if given its slope and a point?

Tip: Remember, the yy-intercept is always the constant term in the slope-intercept form y=mx+by = mx + b when x=0x = 0.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

y = mx + b

Theorems

Slope-Intercept Form of a Line

Suitable Grade Level

Grades 6-8