Math Problem Statement

A line has a slope of 0 and a y-intercept of – 7 3 . Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.

Solution

The slope-intercept form of a line's equation is given by:

y=mx+by = mx + b

where:

  • mm is the slope, and
  • bb is the y-intercept.

In this case, the slope m=0m = 0, and the y-intercept b=73b = -\frac{7}{3}.

Since the slope is 0, the equation simplifies to:

y=73y = -\frac{7}{3}

This is the equation of a horizontal line.

Would you like further explanation or have any questions?

Here are 5 related questions to consider:

  1. What is the equation of a line with a slope of 2 and a y-intercept of 14\frac{1}{4}?
  2. How does the graph of a line change if its slope increases?
  3. What is the meaning of a slope of 0 in the context of a graph?
  4. How would the equation change if the y-intercept were positive instead of negative?
  5. Can you determine the x-intercept of the line from this equation?

Tip: A line with a slope of 0 is always horizontal, and its equation will always be y=by = b.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Slope-intercept form: y = mx + b

Theorems

Equation of a horizontal line theorem

Suitable Grade Level

Grades 6-8