Math Problem Statement

Graph y = x + 3 and identify the x-intercept.

Solution

To determine the x-intercept of the equation y=x+3y = x + 3, we set y=0y = 0, because the x-intercept is the point where the graph crosses the x-axis (and y=0y = 0 at that point).

  1. Substitute y=0y = 0 into y=x+3y = x + 3: 0=x+30 = x + 3

  2. Solve for xx: x=3x = -3

Thus, the x-intercept is at (3,0)(-3, 0).

Would you like me to help with graphing this equation or any additional details?

Here are 5 related questions to expand your understanding:

  1. How do you determine the y-intercept of a line?
  2. What is the slope of the line y=x+3y = x + 3, and how does it affect the graph?
  3. How do you graph a line step-by-step on a coordinate plane?
  4. What does the slope-intercept form of a line (y=mx+by = mx + b) tell you about a graph?
  5. How can you verify the solution for the x-intercept graphically?

Tip: The slope mm in y=mx+by = mx + b tells you how steep the line is, and the bb represents where the line crosses the y-axis.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Graphing
Coordinate Geometry

Formulas

Slope-intercept form: y = mx + b

Theorems

Properties of Linear Equations

Suitable Grade Level

Grades 6-8