Math Problem Statement

Write an equation in slope-intercept form for the given line described. Also, calculate Carmen's earnings for delivering pamphlets, and find equations of lines passing through specific points or under specific conditions.

Solution

It looks like you have uploaded a worksheet covering various linear equations topics, including:

  1. Writing equations in slope-intercept form given the slope and a point.
  2. Finding the equation of a line that passes through a given pair of points.
  3. Applying math to write equations under specific conditions (e.g., perpendicular or parallel to another line).

Would you like help with a specific question, or an explanation on how to approach these types of problems?

Here’s how we can tackle these questions in general:

  1. For slope-intercept form (e.g., questions 10–17): Use the form y=mx+by = mx + b, where mm is the slope and bb is the y-intercept. Plug in the given point to solve for bb.
  2. For finding the equation of a line between two points (e.g., questions 19–24): First, calculate the slope using m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}, then use the slope and one point in the equation y=mx+by = mx + b to find bb.
  3. For perpendicular/parallel lines (e.g., questions 25–28): Use the fact that parallel lines have equal slopes, while perpendicular slopes are negative reciprocals (if mm is the slope, then the perpendicular slope is 1m-\frac{1}{m}).

Let me know which problem you’d like me to solve or explain further!


Five Related Questions:

  1. How do you find the slope if you only have two points?
  2. What is the significance of the y-intercept in a linear equation?
  3. How do you convert between point-slope form and slope-intercept form?
  4. What changes when a line is parallel versus perpendicular to another line?
  5. How can you quickly determine if two lines are parallel or perpendicular based on their equations?

Quick Tip:

To easily find the slope between two points, remember the formula m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}, and practice simplifying fractions to make calculations easier.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope-Intercept Form
Parallel and Perpendicular Lines
Slope Formula

Formulas

Slope-intercept form: y = mx + b
Slope between two points: m = (y2 - y1) / (x2 - x1)
Perpendicular slopes: m1 * m2 = -1

Theorems

Slope formula
Parallel and perpendicular line conditions

Suitable Grade Level

Grades 8-10