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Edexcel GCSE Mathematics
2. Algebra
2.4 Graphs
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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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