2.4 Graphs

• 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.