Math Problem Statement
Solution
To find the equation of the line in the form , we need to determine the slope () and the y-intercept () of the line.
Step 1: Determine the slope ()
The slope of the line is calculated using two known points on the line. Looking at the graph, we can extract two points:
- Point 1:
- Point 2:
The formula for slope is:
Substitute the coordinates:
So, the slope .
Step 2: Determine the y-intercept ()
The y-intercept () is where the line crosses the y-axis. From the graph, we can see that the line crosses the y-axis at , so .
Final equation of the line:
Now that we have and , the equation of the line is:
Would you like more details on any step or have any other questions?
Here are 5 related questions:
- How can you find the slope of a line if only given the graph?
- How does changing the slope () affect the appearance of a line?
- What is the significance of the y-intercept in a linear equation?
- How can you determine if two lines are parallel by looking at their equations?
- What is the effect of changing the y-intercept () on the graph of a line?
Tip: The slope () tells us how steep the line is; a larger slope means a steeper line, while the sign of the slope indicates whether the line goes up or down as increases.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope and Intercept
Coordinate Geometry
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Equation of a line: y = mx + c
Theorems
Slope-Intercept Form
Suitable Grade Level
Grades 8-10