Math Problem Statement

Chapter 3 Test - Written Portion (no key) (1).docx

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Solution

The document contains a set of mathematical problems involving algebra and geometry. Here’s a breakdown of the questions for clarity:

  1. Find the slope of the line that passes through the points (7, -2) and (-9, 5).
  2. Graph the function by finding the x- and y-intercepts of x=3yx = -3y.
  3. Graph the intersection of two inequalities: 2x+y5-2x + y \leq 5 and xy2x - y \geq -2.
  4. Find an equation of a line that is perpendicular to 5x7y=55x - 7y = 5 and passes through (3, 4). The equation should be written in standard form.
  5. Write the equation of a line with a slope of -3 that passes through the point (-7, -3). The equation should be in slope-intercept form y=mx+by = mx + b.
  6. Graph the function by finding the x- and y-intercepts of x24y=24x - 24y = 24.
  7. Solve the word problem: The cost of a tow truck service is modeled by the linear function y=2x+80y = 2x + 80, where yy is the cost in dollars and xx is the number of miles towed. Interpret the slope and y-intercept of this linear equation.

Would you like a solution to all the questions, or is there a specific one you'd like to start with?

Here are 5 related questions for practice:

  1. How do you calculate the slope between two points?
  2. What is the process to find x- and y-intercepts from an equation?
  3. How can you graph systems of inequalities?
  4. How do you determine the equation of a perpendicular line?
  5. How is the slope of a line interpreted in word problems?

Tip: To find the slope of a line through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2), use the formula m=y2y1x2x1.m = \frac{y_2 - y_1}{x_2 - x_1}.

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Math Problem Analysis

Mathematical Concepts

Algebra
Geometry
Linear Equations
Systems of Inequalities

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)
Standard form of a line: Ax + By = C
Slope-intercept form: y = mx + b

Theorems

Parallel and Perpendicular Line Theorem
Linear Function Interpretation

Suitable Grade Level

Grades 9-11