Math Problem Statement
Write the equation for the graphed line
Solution
To find the equation of the line graphed in the image, we need to determine two key components: the slope and the y-intercept. The equation of a line in slope-intercept form is:
where:
- is the slope,
- is the y-intercept.
Step 1: Find the Slope (m)
The slope of a line is calculated as the change in divided by the change in between two points on the line:
From the image, two points on the line are:
Using these points:
Step 2: Identify the y-Intercept (b)
The y-intercept is where the line crosses the y-axis. From the point , we can see that the line crosses the y-axis at . Therefore, .
Step 3: Write the Equation
Now that we know the slope and the y-intercept , we can write the equation of the line:
Final Answer
The equation of the graphed line is:
Would you like a breakdown of how to apply this to other problems, or have any other questions?
Related Questions
- How do you find the equation of a line if only given two points?
- What are different forms of a linear equation (e.g., point-slope, standard form)?
- How would you graph a line given its equation?
- How can you find the x-intercept of a line from its equation?
- What are parallel and perpendicular slopes?
Tip
To check your answer, substitute one of the points into your equation to ensure it satisfies the line equation.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope-Intercept Form
Formulas
y = mx + b
Slope formula m = (y2 - y1) / (x2 - x1)
Theorems
-
Suitable Grade Level
Grades 7-9
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