Math Problem Statement

Identify the slope and y-intercept of the line below

Identify the slope and y-intercept of the line below

Solution

I can see the image of your Algebra test question, which asks you to identify the slope and y-intercept of the given line.

Step 1: Identify Two Points on the Line

From the graph, I will identify two points where the line crosses grid intersections. It appears that the line passes through:

  • (0, 3) (this is the y-intercept)
  • (3, 0) (another point on the line)

Step 2: Calculate the Slope

The formula for slope mm is:

m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

Using the points (0,3)(0,3) and (3,0)(3,0):

m=0330=33=1m = \frac{0 - 3}{3 - 0} = \frac{-3}{3} = -1

Step 3: Identify the Y-Intercept

The y-intercept is the point where the line crosses the y-axis. From the given points, the line crosses the y-axis at (0,3), so:

b=3b = 3

Final Answer:

  • Slope m=1m = -1
  • Y-Intercept b=3b = 3

Would you like a more detailed explanation or graphing steps?

Here are 5 related questions for practice:

  1. How do you determine the slope from a graph using rise over run?
  2. If a line has a positive slope, what does it mean about its direction?
  3. What does a slope of 0 indicate about a line?
  4. How do you write the equation of a line given the slope and one point?
  5. What happens to the graph of a line when you change its y-intercept?

Tip:

A negative slope means the line slants downwards from left to right.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope and Intercept

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)
Equation of a line: y = mx + b

Theorems

Slope-Intercept Form

Suitable Grade Level

Grades 7-9