Slopes - Slope Intercept Form Flashcards
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Questions and Answers

What does the formula for slope $m$ represent?

  • m = x2 - x1 / y2 - y1
  • Both A and C (correct)
  • m = y2 - y1 / x2 - x1
  • m = rise / run

What does the 'rise' refer to in the slope formula?

The change in the y-coordinate between two points.

What are ordered pairs?

Pairs of numbers written in the form (x, y) representing points on a graph.

How is slope calculated using the points (4,2) and (6,4)?

<p>m = 1 (B)</p> Signup and view all the answers

The slope-intercept form is given by the equation $y = mx + b$.

<p>True (A)</p> Signup and view all the answers

What does the variable 'b' represent in the slope-intercept form?

<p>The y-intercept of the line.</p> Signup and view all the answers

In the slope formula $m = \frac{y2 - y1}{x2 - x1}$, 'y2' represents the _______ point's y-coordinate.

<p>second</p> Signup and view all the answers

Match the following slope terms with their definitions:

<p>m = Slope of the line y-intercept = The point where the line crosses the y-axis rise = The change in the y-coordinates run = The change in the x-coordinates</p> Signup and view all the answers

What is the purpose of plotting the y-intercept when graphing a line?

<p>It establishes the starting point for drawing the line.</p> Signup and view all the answers

Flashcards

Slope

A numerical representation of a line's steepness, calculated as the ratio of vertical change (rise) to horizontal change (run).

Slope Formula

The formula used to calculate the slope of a line between two points. It involves subtracting the y-coordinates and dividing by the difference in x-coordinates.

Ordered Pair

A pair of numbers (x, y) that represents a point's location on a graph. The first number represents the x-coordinate, and the second represents the y-coordinate.

Slope-Intercept Form

The equation y = mx + b, where m is the slope, b is the y-intercept, and x and y represent coordinates on a line. It allows for calculating y-values for any x-value.

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Y-intercept

The point where a line crosses the y-axis. It represents the y-coordinate when x is equal to 0.

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Finding Coordinates Using Slope

Using the slope and y-intercept to find the y-coordinate for any given x-value. You start at the y-intercept and move according to the slope to find the corresponding y-value.

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Slope as a Relationship

Represents the relationship between the x and y coordinates on a line. It tells you how much y changes for every change in x.

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Linear Relationship

The concept that for every increase in the x-coordinate, the y-coordinate changes proportionally based on the slope value. This creates a linear relationship between the two variables.

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Slope Direction

Describes the rate at which a line rises or falls. A positive slope indicates an upward trend while a negative slope suggests a downward trend.

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Study Notes

Slope Definition and Calculation

  • Slope (m) represents the steepness of a line, calculated as the ratio of rise (change in y) to run (change in x).
  • The formula for slope is m = (y2 - y1) / (x2 - x1).
  • Ordered pairs (x, y) denote points on a graph, with the first value representing the x-coordinate and the second value the y-coordinate.
  • To determine the slope between two points, apply the formula using the coordinates of the points: for example, from (4, 2) to (6, 4).

Example of Slope Calculation

  • Given ordered pairs example: (4, 2) and (6, 4).
  • The rise calculated is 4 - 2 = 2, and the run calculated is 6 - 4 = 2.
  • Slope (m) calculation: m = (2) / (2) = 1.

Slope-Intercept Form

  • The slope-intercept form of a line is represented by the equation y = mx + b.
  • Here, y signifies the y-coordinate, m is the slope, x is the x-coordinate, and b is the y-intercept (the point where the line crosses the y-axis).
  • The equation helps visualize and draw the graph of the line.

Understanding Slope-Intercept Form

  • The purpose of the slope-intercept form is to calculate the y-coordinate based on a given x-coordinate.
  • The y-intercept (b) provides a starting point on the y-axis from which the slope can be applied.
  • For a slope of 2/1, moving from the y-intercept at (0, 4): for every increase of 1 in x, increase y by 2.

Finding Coordinates Using Slope

  • To find y for a specific x-value using the slope: start at the y-intercept and use the slope to find the corresponding y-coordinate.
  • For x = 1, starting from y = 4 and applying the slope (rise/run), you calculate the new y-coordinate.
  • By continuing this process, you can identify the y-coordinate for any x-value based on the slope.

Conceptual Understanding of Slope

  • Slope indicates how a line rises or falls, reflecting the relationship between x and y coordinates.
  • Each increment in x generates a proportional change in y based on the slope value, illustrating a linear relationship between the two variables.

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Description

This quiz features flashcards that explain the concept of slope, represented by the formula m = (y2 - y1) / (x2 - x1). It covers the definition of slope, how to calculate it through rise over run, and the significance of ordered pairs in graphing points. Perfect for students learning about the basics of linear equations and graphing.

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