Math Problem Statement
The equation of line T, shown below, can be written in the form y = mx + с. What are the values of m and c? Give each of your answers as an integer or as a fraction in its simplest form. Line T 5 4 3 2 1
5-4-3-2-10 1 2 3 4 5 -2 -3 -4- -54
Solution
To determine the values of (the slope) and (the y-intercept) for line from the graph, follow these steps:
1. Identify Two Points on the Line
Choose two points through which the line passes to calculate the slope. From the graph, it looks like line passes through these points:
- Point 1:
- Point 2:
2. Calculate the Slope
The slope of a line through two points and is calculated as: Substitute the points: So, .
3. Find the Y-Intercept
The y-intercept is the y-coordinate when . From Point 2, we see that is on the line, meaning:
Conclusion
The equation of line is: where:
Would you like more details or have any questions?
Related Questions
- How do you find the equation of a line given two points?
- What does the slope represent in the context of a line?
- How can you convert an equation in standard form to slope-intercept form?
- What happens to the graph of a line if the slope is negative?
- How does the y-intercept affect where the line crosses the y-axis?
Tip
To find the slope between two points accurately, always ensure they are clear intersections on the graph for precision.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Coordinate Geometry
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Slope-intercept form: y = mx + c
Theorems
Point-Slope Theorem
Slope-Intercept Form
Suitable Grade Level
Grades 8-10