Math Problem Statement
Solution
To find the equation of the line, we need to determine both the slope (denoted as ) and the y-intercept (the constant term in the equation ).
Step 1: Identify the slope
The slope of the line can be calculated by choosing two points on the line. From the image, the points and are on the line.
The slope is given by the formula: Substituting the coordinates of the points:
So, the slope is .
Step 2: Identify the y-intercept
The y-intercept is where the line crosses the y-axis. From the graph, it appears the line crosses the y-axis at .
Step 3: Write the equation
Substituting the slope and y-intercept into the equation : This simplifies to:
This is the equation of the line.
Would you like more details on any part of this process, or do you have any further questions?
Here are some follow-up questions you might find interesting:
- How do you calculate the slope when given two arbitrary points?
- What is the significance of the y-intercept in the equation of a line?
- Can a line have a slope of 0 or undefined? What do these cases represent?
- How can you determine the equation of a line if it is parallel or perpendicular to another line?
- What changes in the equation when the line is shifted up or down on the graph?
Tip: Always check the points you use for calculating the slope to ensure they are accurate; even a small mistake in the coordinates can lead to incorrect results.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope-Intercept Form
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Equation of a line: y = mx + c
Theorems
Linear Equation
Suitable Grade Level
Grades 8-10