Math Problem Statement
Solution
The image shows a straight line on a graph, and the question asks to find the values of (the slope) and (the y-intercept) of the line. Here's how we can solve this:
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Find the slope : The slope of a line is calculated using the formula: We need two points on the line. From the graph, we can identify:
- Point 1: (the y-intercept)
- Point 2:
Using these points:
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Find the y-intercept : The y-intercept is where the line crosses the y-axis. From the graph, it's clear the line crosses at , so .
Thus, the values of and are:
Would you like more details or have any questions about these calculations?
Here are 5 related questions you can explore:
- How do you find the slope of a line if given different points?
- What happens to a line if the slope is positive vs. negative?
- Can you explain the relationship between the slope and the steepness of a line?
- How do parallel and perpendicular slopes relate to each other?
- How can the equation of a line change if shifted up or down on the y-axis?
Tip: When identifying the slope, always choose two points that are easy to read from the graph to avoid mistakes in calculations.
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Slope-Intercept Form
Formulas
m = (y2 - y1) / (x2 - x1)
y = mx + b
Theorems
Slope Formula
Y-Intercept in Linear Equations
Suitable Grade Level
Grades 8-10