Linear Functions and Slope Calculations
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Questions and Answers

What is the slope of the linear function $y = -4 - \frac{3}{2}x$?

  • -4
  • 0
  • -\frac{3}{2} (correct)
  • \frac{2}{3}

    • Which point does not lie on the graph of the function $y = -4 - \frac{3}{2}x$?

  • (4, 10) (correct)
  • (2, 7)
  • (0, -4)
  • (-2, -1)

    • What is the y-intercept of the function $y = -4 - \frac{3}{2}x$?

  • -4 (correct)
  • -3
  • 4
  • 0

    • If $x$ is increased by 4, what will be the change in $y$ based on the function $y = -4 - \frac{3}{2}x$?

    <p>Decrease by 12</p> Signup and view all the answers

    What is the domain of the function $y = -4 - \frac{3}{2}x$ if restricted to the table of values provided?

    <p>x \in { -4, -2, 0, 2 }</p> Signup and view all the answers

    What is the slope of the line that passes through the points (0, -1) and (3, 2)?

    <p>0.5</p> Signup and view all the answers

    If the rise of the triangle on the graph is 3 units, what is the run based on the provided information?

    <p>6 units</p> Signup and view all the answers

    Which of the following statements about the slope of the line is true?

    <p>The slope indicates an uphill direction.</p> Signup and view all the answers

    What does the term 'rise' refer to in the context of slope calculations?

    <p>The vertical change in the graph.</p> Signup and view all the answers

    Given the slope of 1/2, how would you interpret this in terms of rise and run?

    <p>For every 1 unit of rise, there is 2 units of run.</p> Signup and view all the answers

    What is the slope calculated from the points (-6, -14) and (18, -20)?

    <p>-1/4</p> Signup and view all the answers

    Using the points (-8, 5) and (10, 15), what is the correct formula application to find the slope?

    <p>slope = (15 - 5) / (10 - (-8))</p> Signup and view all the answers

    What is the simplified result of the slope from the calculation slope = (15 - 5) / (10 - (-8))?

    <p>5/9</p> Signup and view all the answers

    If the coordinates (x₁, y₁) are (-8, 5) and (x₂, y₂) are (10, 15), which of the following describes a common mistake in calculating the slope?

    <p>Mistaking the formula as (x₂ - x₁) / (y₂ - y₁)</p> Signup and view all the answers

    Which slope is steeper based on the examples provided?

    <p>5/9 from points (-8, 5) and (10, 15)</p> Signup and view all the answers

    What is the slope of the line represented by the equation $y = 2x - 3$?

    <p>2</p> Signup and view all the answers

    What is the y-intercept of the line defined by the equation $y = 2x - 3$?

    <p>-3</p> Signup and view all the answers

    If a point on the line is (3, 0), what can be inferred about its significance?

    <p>It is the x-intercept of the line.</p> Signup and view all the answers

    Given the slope of the line is 2, what is the change in y when x increases by 1?

    <p>2</p> Signup and view all the answers

    Which of the following equations represents a line with the same slope and y-intercept as the original line?

    <p>$y = 2x - 3$</p> Signup and view all the answers

    What is the standard form of the equation that corresponds to the x-intercept (6,0) and y-intercept (0,-4)?

    <p>2x + y = 8</p> Signup and view all the answers

    Which equation represents the same line as -8x - 4y = -16?

    <p>2x + y = 4</p> Signup and view all the answers

    What are the coordinates of the x-intercept given the intercept form derived from the equation -8x - 4y = -16?

    <p>(6,0)</p> Signup and view all the answers

    If we rearrange -8x - 4y = -16 into slope-intercept form, what would the slope be?

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

    What is the value of C in the equation Ax + By = C when the line passes through the points (6,0) and (0,-4)?

    <p>-16</p> Signup and view all the answers

    What is the effect of a slope that is a whole number on the graph of a linear function?

    <p>It makes the graph steeper.</p> Signup and view all the answers

    In the point-slope form of a linear function, what does the variable 'm' represent?

    <p>The rate of change in y with respect to x.</p> Signup and view all the answers

    Which of the following equations represents a linear function with a negative slope?

    <p>y = -2x + 5</p> Signup and view all the answers

    How does a fraction slope affect the steepness of a linear function's graph?

    <p>It makes the graph flatter.</p> Signup and view all the answers

    What does the equation y - y₁ = m(x - x₁) signify in terms of graphing a linear function?

    <p>It expresses the linear relationship between x and y at a specific point.</p> Signup and view all the answers

    What is the slope of the line represented by the equation 6x + 4y = 8 when converted to slope-intercept form?

    <p>-3/2</p> Signup and view all the answers

    What is the y-intercept of the line given by -15x - 3y = -6 once it is in slope-intercept form?

    <p>2</p> Signup and view all the answers

    When converting the equation 5y + 25x = 25 into slope-intercept form, what is the resulting simplified form?

    <p>y = -5x + 5</p> Signup and view all the answers

    What happens to the signs of the coefficients when converting from standard form to slope-intercept form if they are negative?

    <p>They become positive in slope-intercept form</p> Signup and view all the answers

    If the equation 4x + 2y = 8 is converted to slope-intercept form, what is the final slope of the line?

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

    What is the first step in converting the point-slope form equation y - 8 = $ rac{1}{2}$(x + 2) to slope-intercept form?

    <p>Distribute $ rac{1}{2}$ into the equation</p> Signup and view all the answers

    What is the value of the y-intercept in the equation y = $ rac{1}{2}$x + 9?

    <p>9</p> Signup and view all the answers

    What is the slope of the line represented by the equation y = -3x + 5?

    <p>-3</p> Signup and view all the answers

    After simplifying y - 12 = -3(x + 5/3) - 2, what is the resulting expression for y?

    <p>y = -3x + 5</p> Signup and view all the answers

    In the context of converting point-slope form to slope-intercept form, what does 'm' represent?

    <p>The slope of the line</p> Signup and view all the answers

    What is the slope of the equation represented in slope-intercept form from Equation 4 (3y = -10)?

    <p>-1.5</p> Signup and view all the answers

    What would be the value of y in Equation 5 (-3x + y = ?) if x = 6?

    <p>18</p> Signup and view all the answers

    Which equation, when converted to slope-intercept form, has a y-intercept of 24?

    <p>2x + 3y = 24</p> Signup and view all the answers

    What is the first step to convert Equation 2 (48 - 4y = 76 - 48) to slope-intercept form?

    <p>Simplify the right side</p> Signup and view all the answers

    After converting Equation 1 (3x - x + 48 = 3) to slope-intercept form, what will be the resulting equation?

    <p>y = -2x + 45</p> Signup and view all the answers

    What is the equation of the line parallel to $y=3x+8$ that passes through the point $(-3, 7)$?

    <p>$y=3x+4$</p> Signup and view all the answers

    Which of the following pairs of slopes indicate that two lines are perpendicular?

    <p>$ rac{3}{4}$ and $- rac{4}{3}$</p> Signup and view all the answers

    If a line has the equation $y = - rac{2}{5}x + 5$, which of the following equations represents a line that is parallel to it?

    <p>$y = - rac{2}{5}x - 3$</p> Signup and view all the answers

    Which equation correctly illustrates two lines that are perpendicular to each other?

    <p>$y = rac{1}{3}x - 1$ and $y = -3x + 5$</p> Signup and view all the answers

    What can be concluded about the slopes of the lines given by the equations $y = -7x + 2$ and $y = 0.14x - 5$?

    <p>The lines are parallel.</p> Signup and view all the answers

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