Math Problem Statement
Solution
The problem shown in the image asks for the equation of the line represented on the graph. Let's go through the steps to find the equation of this line.
Step 1: Identify Two Points on the Line
From the graph, the line passes through two clear points:
- Point 1:
- Point 2:
Step 2: Calculate the Slope (m)
The slope of a line is given by the formula: Using the points and , we can substitute: Thus, the slope .
Step 3: Use the Slope-Intercept Form
The equation of a line in slope-intercept form is: We already know , and we can use the point , where the line crosses the y-axis, to find , the y-intercept.
Since the y-intercept is the point where , we can see that .
Final Equation
Substituting and into the slope-intercept form:
So, the equation of the line is:
Let me know if you need any clarifications or further details.
Questions to Explore:
- What is the slope of a horizontal line?
- How does changing the slope affect the steepness of a line?
- What happens to the equation of a line if the slope is zero?
- How can you find the slope of a line given only its graph?
- Can a line have a positive y-intercept and a negative slope?
Tip: Always use two clear points to calculate the slope to avoid mistakes!
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope-Intercept Form
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Slope-Intercept Form: y = mx + b
Theorems
Linear Equation Theorem
Suitable Grade Level
Grades 6-8