Page 102 - Knowledge Organiser Yr8 24-25

Knowledge Base: Mathematics TOPIC 21: Graphing Equations Year 8 | Summer Term 1
By the end of this topic you should be able to:
• Substitute values into an equation or formula
• Work with and identify the key features of a linear graph in the form y = mx + c
• Find the midpoint of 2 coordinates
• Switch between explicit and implicit equations
• Recognize the gradient of parallel and perpendicular lines
• Plot curved graphs
Linear function
A function whose graph is always a straight line
y = mx + c
Language
Meaning
Example
Formula
A rule connecting different quantities. You can write a formula in words or symbols
Length = Width plus three L = W+ 3
Gradient
The slope of a line
If y = mx + c
Then m is the gradient
Intercept
Where a line touches the x-axis or y-axis
If y = mx + c
Then c is the y-axis intercept
Midpoint
The point that lies half-way between its 2 endpoints
The midpoint of the line joining (1,4) and (7,8) is (4,6)
Line segment
A line between 2 set points
The line between (1,4) and (7,8) is a line segment
Important things to remember:
The graph of the equation y = mx+c is a straight line with a gradient of m and a y intercept of c
Parabola Explicit function
The shape you get if you plot a quadratic function An equation where y is the subject
y = x2
y = 2x + 1 y = mx + c y = 3x2
Implicit function
An equation where y is not the subject
2y + 3x = 5 y – c = mx
Worked examples
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