Math Problem Statement
Identify the slope and the y-intercept of the line graphed below. Then, write the equation of the line in slope-intercept form.
Solution
Let's analyze the graph to determine the slope, y-intercept, and equation of the line.
Step 1: Identifying the Slope
From the graph, the line passes through two clear points. Let's use the points:
- Point 1:
- Point 2:
The slope formula is: Substitute the points and : So, the slope .
Step 2: Identifying the Y-Intercept
The y-intercept is where the line crosses the y-axis. From the graph, it is clear that the line crosses the y-axis at . So, the y-intercept .
Step 3: Writing the Equation in Slope-Intercept Form
The slope-intercept form of a line is: Substituting and :
Final Answer:
- Slope:
- Y-Intercept:
- Equation of the Line:
Would you like further explanation or have any questions?
Here are 5 related questions to explore:
- What is the slope of a line parallel to this one?
- How do you find the equation of a line given two points?
- How do you determine the slope if the line is vertical?
- What does the slope of a line tell you about its steepness?
- How do you graph a line using its slope and y-intercept?
Tip: In slope-intercept form, the slope determines how steep the line is, and the y-intercept tells where the line crosses the y-axis.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Slope-Intercept form: y = mx + b
Theorems
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Suitable Grade Level
Grades 7-9