2.4 Graphs

• Linear graphs are graphs that form a straight line.
• The y-intercept of a linear graph is the point where the graph crosses the x-axis.

  False
• What is the formula to find the slope of a linear graph using two points?

  $m =$$\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$
• The point-slope form of a linear equation is $y - y_{1} =$$m(x - x_{1})$, where $(x_{1}, y_{1})$ is a known point on the line.
• The y-intercept is the y-coordinate when x = 0.


  True
• What does the slope of a line represent?

  The steepness
• The y-intercept of a linear graph is the point where the graph crosses the y-axis.


  True
• The y-intercept in the equation $y =$$mx +$$c$ is represented by the variable c
• What should you substitute into the equation $y =$$mx +$$c$ to find the y-intercept?


  A point and the gradient
• What is the equation used in the slope-intercept form of a linear graph?

  $y =$$mx +$$c$
• If a line passes through (1, 4) and has a gradient of 3, what is its equation in slope-intercept form?

  $y =$$3x +$$1$
• What is the slope-intercept form of a linear equation used for plotting a graph?

  $y =$$mx +$$c$
• What is the general form of a quadratic equation?

  $y =$$ax^{2} +$$bx +$$c$
• How is the x-coordinate of the vertex of a parabola calculated?

  $x =$$- \frac{b}{2a}$
• What is the general form of a quadratic equation?

  $y =$$ax^{2} +$$bx +$$c$
• x-intercepts of a quadratic graph are found by setting $y =$$0$ and solving for $x$.


  True
• The x-coordinate of the vertex is given by $x =$$- \frac{b}{2a}$.vertex
• The axis of symmetry of a parabola is a vertical line that passes through the vertex.


  True
• What is the condition for a quadratic graph to have a maximum value?

  $a < 0$
• The turning point of a parabola is called the vertex
• What does the coefficient 'a' determine in a quadratic equation?

  Orientation and steepness
• What does the coefficient 'c' determine in a quadratic equation?

  Y-intercept
• Linear graphs are defined by the equation $y =$$mx +$$c$.


  True
• What does the y-intercept 'c' represent in a linear graph?

  Point where line crosses y-axis
• What is the gradient of a linear graph also called?

  Slope
• The equation of a linear graph is typically written as $y =$$mx +$$c$, where $m$ is the gradient and $c$ is the y-intercept.
• Match the key concepts with their descriptions:

  Slope ↔️ $m =$$\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

  Y-intercept ↔️ Point where the graph crosses the y-axis
• What does the gradient of a linear graph represent?

  Steepness
• The general equation of a linear graph is $y =$$mx +$$c$, where $c$ represents the y-intercept.
• The slope of a line is calculated as the change in y-value divided by the change in x
• In the equation y = mx + c</latex>, what does 'm' represent?

  The gradient
• The formula for calculating the gradient (m) between two points is $m =$$\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$.


  True
• The formula for the gradient (m) is m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}</latex>, and the formula for the y-intercept (c) is $c =$$y - m$x
• The point-slope form of a linear graph requires a known point and the gradient to determine the equation.


  True
• In the slope-intercept form, the gradient is represented by the variable m
• The y-intercept is the point where the line crosses the y-axis.


  True
• The x-intercepts of a quadratic graph are found by setting $y =$$0$ and solving for x
• The axis of symmetry of a parabola passes through its vertex.


  True
• The graph of a quadratic equation is called a parabola
• The y-intercept of a quadratic graph is found by setting $x =$$0$ in the equation.


  True