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
Solution
The graph you provided represents a straight line, which can be described by the equation of the form , where:
- is the slope of the line, and
- is the y-intercept (the value of when ).
Step 1: Find the slope
The slope is calculated as: From the graph, the line passes through points and .
So, the slope is:
Step 2: Find the y-intercept
Looking at the graph, the line intersects the y-axis at , so the y-intercept .
Step 3: Equation of the line
Using and , the equation of the line is:
Therefore, the correct equation is:
B. .
Would you like more details or have any questions?
Here are five related questions for further exploration:
- How do you find the slope of a line given two points?
- What does the y-intercept represent in a graph?
- How can you graph a linear equation if you know its slope and y-intercept?
- How does changing the slope affect the steepness of the line?
- 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