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 mm (the slope) and cc (the y-intercept) for line TT 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 TT passes through these points:

  • Point 1: (4,1)(-4, -1)
  • Point 2: (0,3)(0, 3)

2. Calculate the Slope mm

The slope mm of a line through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is calculated as: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} Substitute the points: m=3(1)0(4)=3+14=44=1m = \frac{3 - (-1)}{0 - (-4)} = \frac{3 + 1}{4} = \frac{4}{4} = 1 So, m=1m = 1.

3. Find the Y-Intercept cc

The y-intercept cc is the y-coordinate when x=0x = 0. From Point 2, we see that (0,3)(0, 3) is on the line, meaning: c=3c = 3

Conclusion

The equation of line TT is: y=x+3y = x + 3 where:

  • m=1m = 1
  • c=3c = 3

Would you like more details or have any questions?

Related Questions

  1. How do you find the equation of a line given two points?
  2. What does the slope represent in the context of a line?
  3. How can you convert an equation in standard form to slope-intercept form?
  4. What happens to the graph of a line if the slope mm is negative?
  5. How does the y-intercept cc 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