2.4 Graphs

    Cards (48)

    • The most common coordinate system is the Cartesian
    • To plot a point on a Cartesian plane, we use an ordered pair of coordinates in the form (x, y)
    • The general form of a linear equation is y = mx + b
    • Understanding the slope and y-intercept is key to graphing and interpreting linear equations
    • The gradient of a line is calculated using the formula m = (y2 - y1) / (x2 - x1)
    • The y-intercept of a line is the point where it crosses the x-axis.
      False
    • The y-intercept is the y-value when x equals 0.
    • To plot a point on a Cartesian plane, we use an ordered pair of coordinates (x, y).
      True
    • Steps to graph a linear equation:
      1️⃣ Plot the y-intercept (b) on the y-axis.
      2️⃣ Use the slope (m) to find another point on the line.
      3️⃣ Draw a straight line through the two points.
    • To find the gradient and y-intercept, convert the equation to the form y = mx + b.
    • The y-intercept shifts the line up or down on the graph.

      True
    • A quadratic equation is of the form `y = ax^2 + bx + c`, where `a`, `b`, and `c` are constants
    • The roots of a parabola are its x-intercepts, where `y =` 0
    • The axis of symmetry for the parabola y = x^2 - 4x + 3 is x = 2.

      True
    • To graph a parabola, first plot the vertex
    • What do the coordinates of the intersection point represent when solving simultaneous equations graphically?
      The solution
    • The Cartesian coordinate system is divided into four quadrants with unique combinations of positive and negative x and y values

      True
    • The x-coordinate represents the horizontal position, and the y-coordinate represents the vertical position

      True
    • What does 'm' represent in the equation y = mx + b?
      Slope
    • The gradient of a line can be calculated directly from its equation in the form y = mx + b

      True
    • The line y = 2x + 3 crosses the y-axis at the point (0, 3)

      True
    • The line `y = 2x + 3` has a y-intercept of 3
    • The Cartesian coordinate system uses a 2D grid with an x-axis and a y-axis.

      True
    • The general form of a linear equation is y = mx + b.
    • A line with a positive slope slants upward.
    • The gradient of a line passing through (1, 5) and (3, 9) is 2.

      True
    • A quadratic equation of the form `y = ax^2 + bx + c` produces a parabola when graphed.
    • The vertex of a parabola is its highest or lowest point.

      True
    • Steps to graph a quadratic equation
      1️⃣ Find the vertex using the formula `x = -b / (2a)`
      2️⃣ Find the axis of symmetry using the x-coordinate of the vertex
      3️⃣ Create a table of values around the vertex to plot points
      4️⃣ Draw the parabola through the plotted points
    • What is the value of y when x = 3 for the equation y = x^2 - 4x + 3?
      0
    • If the coefficient of x^2 is negative, the parabola opens downward.

      True
    • The graphical method is highly accurate for all types of equations.
      False
    • What is a coordinate system used for?
      Locating points
    • Match each quadrant with its corresponding x and y values:
      Quadrant I ↔️ Positive x, Positive y
      Quadrant II ↔️ Negative x, Positive y
      Quadrant III ↔️ Negative x, Negative y
      Quadrant IV ↔️ Positive x, Negative y
    • Arrange the following steps to describe how to plot a point on a Cartesian plane:
      1️⃣ Move horizontally according to the x-coordinate
      2️⃣ Move vertically according to the y-coordinate
      3️⃣ Mark the point where the movements intersect
    • The y-intercept is the point where the line crosses the y-axis

      True
    • What effect does a positive gradient have on the line?
      Slants upward
    • The formula for the gradient of a line is m
    • The gradient of a line represents its steepness and is calculated using two points on the line.

      True
    • Understanding quadrants is crucial for locating points on a 2D plane.
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