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Finding Slope in Precalculus

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  • What is the formula to find the slope given two points?
    The slope \(m\) is \(\frac{y_2 - y_1}{x_2 - x_1}\), where (x₁, y₁) and (x₂, y₂) are the two points.
  • How do you find slope from a graph?
    Identify two points on the line, then use the slope formula \(\frac{\Delta y}{\Delta x}\) by counting vertical and horizontal changes.
  • How to find slope from a table of values?
    Calculate the change in y-values divided by the change in x-values between two points in the table.
  • How to find slope from a verbal description?
    Identify how much y changes for a given change in x, then express slope as rise over run.
  • What does a positive slope indicate?
    The line rises from left to right, meaning y increases as x increases.
  • What does a negative slope indicate?
    The line falls from left to right, meaning y decreases as x increases.
  • What is the slope of a horizontal line?
    The slope is zero because there is no vertical change.
  • What is the slope of a vertical line?
    The slope is undefined because the change in x is zero.
  • How to interpret slope as a rate of change?
    Slope represents how much y changes for each unit increase in x.
  • What is the slope of the line through points (3, 4) and (7, 12)?
    Slope is \(\frac{12 - 4}{7 - 3} = \frac{8}{4} = 2\).
  • How to find slope if given a table with points (1, 5) and (4, 11)?
    Slope is \(\frac{11 - 5}{4 - 1} = \frac{6}{3} = 2\).
  • If a line passes through (2, 3) and (2, 7), what is the slope?
    Slope is undefined because \(x_2 - x_1 = 0\).
  • If a line passes through (1, 6) and (5, 6), what is the slope?
    Slope is zero because \(y_2 - y_1 = 0\).
  • How to find slope from a verbal description: 'The line rises 3 units for every 2 units it runs to the right'?
    Slope is \(\frac{3}{2}\).
  • What does zero slope mean about the line's direction?
    The line is perfectly horizontal.
  • What does an undefined slope mean about the line's direction?
    The line is perfectly vertical.
  • How to find slope from a graph with points (0, 0) and (4, 8)?
    Slope is \(\frac{8 - 0}{4 - 0} = 2\).
  • What is the slope formula used to calculate?
    The rate of change or steepness of a line between two points.
  • Why can't slope be calculated if \(x_2 = x_1\)?
    Because division by zero is undefined, so slope is undefined.
  • How to find slope from a table with points (2, 3) and (5, 9)?
    Slope is \(\frac{9 - 3}{5 - 2} = \frac{6}{3} = 2\).