Math Problem Statement

Which equation best represents the relationship between x and y in the graph? A.y=3x+3

B.y=3x−1

C.y=13x+3

Which equation best represents the relationship between x and y in the graph? A. y = 3x + 3 B. y = 3x - 1 C. y = 13x + 3

Solution

The graph you provided represents a straight line, which can be described by the equation of the form y=mx+by = mx + b, where:

  • mm is the slope of the line, and
  • bb is the y-intercept (the value of yy when x=0x = 0).

Step 1: Find the slope mm

The slope mm is calculated as: m=change in ychange in xm = \frac{\text{change in } y}{\text{change in } x} From the graph, the line passes through points (1,3)(1, 3) and (2,6)(2, 6).

So, the slope is: m=6321=31=3m = \frac{6 - 3}{2 - 1} = \frac{3}{1} = 3

Step 2: Find the y-intercept bb

Looking at the graph, the line intersects the y-axis at y=0y = 0, so the y-intercept b=1b = -1.

Step 3: Equation of the line

Using m=3m = 3 and b=1b = -1, the equation of the line is: y=3x1y = 3x - 1

Therefore, the correct equation is:

B. y=3x1y = 3x - 1.

Would you like more details or have any questions?


Here are five related questions for further exploration:

  1. How do you find the slope of a line given two points?
  2. What does the y-intercept represent in a graph?
  3. How can you graph a linear equation if you know its slope and y-intercept?
  4. How does changing the slope affect the steepness of the line?
  5. How does the y-intercept shift the graph vertically?

Tip: To verify an equation of a line, you can substitute points from the graph into the equation to see if they satisfy it.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

y = mx + b (Slope-Intercept Form)
Slope formula: m = (y2 - y1) / (x2 - x1)

Theorems

Slope-Intercept Theorem

Suitable Grade Level

Grades 7-9