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 .
The -intercept of a line is the value of when . To find it:
-
Substitute into the equation:
-
Simplify:
Thus, the -intercept of the line is 3.
Would you like further clarification or additional examples? Here are five related questions for further exploration:
- What is the slope of this line, and how is it interpreted geometrically?
- How can the equation be rewritten in standard form ?
- What is the x-intercept of this line, and how is it calculated?
- How would the graph of this line change if the slope were doubled?
- How do you determine the equation of a line if given its slope and a point?
Tip: Remember, the -intercept is always the constant term in the slope-intercept form when .
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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