Math Problem Statement

This is the graph of a linear inequality. Write the inequality in slope-intercept form.

Solution

I see that you've uploaded an image of a graph of a linear inequality. Let's go step by step to determine the inequality in slope-intercept form.

  1. Identify the slope and y-intercept:

    • The line seems to pass through the y-axis at (0, 3), which means the y-intercept b=3b = 3.
    • The slope is determined by identifying two points on the line. I see that the line goes through the point (0, 3) and another point like (2, 1). The slope mm is calculated as: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} Using the points (0, 3) and (2, 1), the slope calculation is: m=1320=22=1m = \frac{1 - 3}{2 - 0} = \frac{-2}{2} = -1
  2. Write the equation: Now, we have the slope m=1m = -1 and the y-intercept b=3b = 3. The equation of the line in slope-intercept form is: y=x+3y = -x + 3

  3. Determine the inequality: Since the graph shows a dashed line, this indicates that the inequality is strict (i.e., << or >>, not \leq or \geq). Also, the shading is above the line, which indicates that the solution is for values greater than the line. Hence, the inequality is: y>x+3y > -x + 3

So, the inequality in slope-intercept form is: y>x+3y > -x + 3

Would you like any further clarification on this process? Let me know if you need more details!

Further Questions:

  1. How do you calculate the slope when the points on the line are not given?
  2. What does the dashed line indicate in terms of the inequality?
  3. How can you interpret the shaded region in relation to the inequality?
  4. How would the inequality change if the line were solid instead of dashed?
  5. What is the difference between linear equations and linear inequalities?

Tip: To find the slope, always use two points on the line and apply the formula m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}.

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Math Problem Analysis

Mathematical Concepts

Linear Inequalities
Slope-Intercept Form
Graphing Inequalities

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)
Slope-Intercept form: y = mx + b

Theorems

Linear Inequality Graphing

Suitable Grade Level

Grades 7-9