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.

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

The slope formula is: slope (m)=y2y1x2x1\text{slope (m)} = \frac{y_2 - y_1}{x_2 - x_1} Substitute the points (0,1)(0, -1) and (2,1)(2, 1): m=1(1)20=1+12=22=1m = \frac{1 - (-1)}{2 - 0} = \frac{1 + 1}{2} = \frac{2}{2} = 1 So, the slope m=1m = 1.

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 y=1y = -1. So, the y-intercept b=1b = -1.

Step 3: Writing the Equation in Slope-Intercept Form

The slope-intercept form of a line is: y=mx+by = mx + b Substituting m=1m = 1 and b=1b = -1: y=1x1or simplyy=x1y = 1x - 1 \quad \text{or simply} \quad y = x - 1

Final Answer:

  • Slope: m=1m = 1
  • Y-Intercept: b=1b = -1
  • Equation of the Line: y=x1y = x - 1

Would you like further explanation or have any questions?

Here are 5 related questions to explore:

  1. What is the slope of a line parallel to this one?
  2. How do you find the equation of a line given two points?
  3. How do you determine the slope if the line is vertical?
  4. What does the slope of a line tell you about its steepness?
  5. How do you graph a line using its slope and y-intercept?

Tip: In slope-intercept form, the slope mm determines how steep the line is, and the y-intercept bb 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