Math Problem Statement
Solution
In this graph, we are tasked with finding the slope, y-intercept, and equation of the line.
1. Finding the Slope:
The slope of a line is given by the formula: From the graph, we can identify two points on the line. Let's say the points are:
- where the line intersects the y-axis.
- another point on the line.
Now, apply the slope formula: So, the slope (m) is -1.
2. Finding the Y-intercept:
The y-intercept is the point where the line crosses the y-axis. From the graph, it's clear that the line crosses the y-axis at . Thus, the y-intercept is .
3. Finding the Equation:
The equation of a line in slope-intercept form is: Where is the slope and is the y-intercept.
Substituting the values: Thus, the equation of the line is:
Summary:
- Slope (m):
- Y-intercept (b):
- Equation:
Would you like more details or have any questions about this? Here are 5 related questions to help expand on this:
- How do you calculate the slope if given two arbitrary points?
- What does the slope of indicate about the line's steepness and direction?
- How would you find the x-intercept of this line?
- Can you convert the equation into standard form?
- How does the graph of this line change if the slope or y-intercept were different?
Tip: When plotting a line from an equation, start by plotting the y-intercept, then use the slope to find another point.
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Slope
Y-Intercept
Equation of a Line
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Slope-intercept form: y = mx + b
Theorems
-
Suitable Grade Level
Grades 7-8
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