Algebra Class: Understanding Slope and Functions
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Questions and Answers

What is the slope of the equation Nate: -3x - 10?

  • -3 (correct)
  • 0
  • 3
  • -10

How can you confirm that the rate of change in a linear equation is constant?

  • By checking the slope between any two points on the line. (correct)
  • By calculating the slope at multiple points.
  • By making a scatter plot of points.
  • By evaluating the y-intercept at varying values of x.

What does a steeper graph indicate about the rate of change?

  • It indicates a slower rate of change.
  • It indicates no change at all.
  • It indicates a faster rate of change. (correct)
  • It indicates variable rate of change.

When finding the rate of change over the interval 4-8, what is being measured?

<p>The change in y relative to the change in x. (A)</p> Signup and view all the answers

What is the significance of finding 'perfect' points on a graph?

<p>They help establish the slope and provide accurate rate of change. (A)</p> Signup and view all the answers

What is the output when the input is 2 and using the rule -x?

<p>-2 (B)</p> Signup and view all the answers

Which of the following defines a function based on the description provided?

<p>A set of input-output pairs with unique x-values. (B)</p> Signup and view all the answers

Given the point (2, 7), what is the value of b in the equation $y=3.5x+b$?

<p>0 (B)</p> Signup and view all the answers

Which type of function represents the graph passing through the points (0, 3) and (10, 3)?

<p>Linear (C)</p> Signup and view all the answers

What is the correct rearrangement of the equation $2y=5x+10$ to isolate y?

<p>y = 2.5x + 5 (D)</p> Signup and view all the answers

What is the slope of the line that goes through points (0, 3) and (10, 3)?

<p>0 (C)</p> Signup and view all the answers

What is the output of the function if the input is x = -2 for the rule defined by -x?

<p>2 (C)</p> Signup and view all the answers

Considering the inequality represented by -5 ≤ x ≤ -3, which interval does this correspond to on the graph?

<p>The region between -5 and -3, inclusive (D)</p> Signup and view all the answers

If a graph shows a straight horizontal line, what can be concluded about the y-coordinates of the points on that line?

<p>All y-coordinates are equal (D)</p> Signup and view all the answers

In the context of the given graph, if the x-axis and y-axis are not marked with scale, which aspect might be difficult to determine?

<p>The actual values of the points plotted (D)</p> Signup and view all the answers

Flashcards

Slope

The steepness of a line, representing how much the y-value changes for every change in the x-value.

Rate of Change

Describes how a quantity changes over time or another variable. In a linear equation, it's constant.

Y-intercept

The point where a line crosses the y-axis. It's the value of y when x is 0.

Linear Equation

An equation that represents a straight line. It has a constant rate of change.

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Find Rate of Change from Graph

To calculate the rate of change on a graph, find two points and divide the difference in y-values by the difference in x-values.

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Input/Output Rule

A rule that describes how an input value is transformed into an output value. The rule can be a simple operation like multiplication, addition, or subtraction. It can be expressed as a formula.

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Function

A relationship between inputs and outputs where each input has exactly one output. No repeating x-values.

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Function Table

A table that organizes input (x) values and their corresponding output (y) values based on a specific function rule.

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Finding the y-intercept

The point where the graph of a function intersects the y-axis. It occurs when x = 0. To find it, set x to 0 in the function's equation and solve for y.

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Function in Standard Form

A function written in the form y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

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Linear Function

A function whose graph is a straight line. Its equation can be written in the form y = mx + c, where m is the slope and c is the y-intercept.

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Non-Linear Function

A function whose graph is not a straight line. It can have curves, bends, or other shapes.

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Slope Formula

The formula used to calculate the slope of a line passing through two points (x1, y1) and (x2, y2): (y2 - y1) / (x2 - x1)

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