Equations and their graphs | Maths | Quizalize & Oak National Academy

Starter quiz

The graph of the linear equation $y=5x-9$ is uniquely defined by a gradient of $5$ and __________ of $-9$ .
- $y$ -axis
- $y$ coordinate
- $y$ intercept ✓
- $y$ solution
Which of these graphs will not form straight line when plotted?
- $y=7x-2$
- $y=2-7x$
- $y=x^2-7$ ✓
- $y=-2x-7$
- $7x+2y=1$
Which of these will be $y$ values if you populated this table for values for the linear equation $y=7-2x$ ?
- -2
- 1 ✓
- 2
- 7 ✓
- 9 ✓
From left to right how will the $y$ values in this table be read if you complete the table for the linear equation $y=4x-9$ ?
- -3, -2, -1, 0, 1, 2, 3
- -17, -13, -9, -5, -1, 3, 7
- -21, -25, -29, -33, -37, -41, -45
- -21, -17, -13, -9, -5, -1, 3 ✓
- 3, -1, -5, -9, -13, -17, -21
The linear graph $3x+5y=25$ is plotted. When the $x$ coordinate is $0$ the $y$ coordinate is ______.
- '5' ✓
The quadratic graph of $y=x^2$ is plotted. When the $x$ coordinate is $-5$ the $y$ coordinate is ______.
- '25' ✓

Exit quiz

An __________ is the coordinate where a line or curve meets a given axis.
- intersection
- intercept ✓
- inverse
Which of these graphs will NOT form straight line when plotted?
- $y=7x-3$
- $y=3-7x$
- $y=x^3-7$ ✓
- $y=-3x-7$
- $7x+y=1$ 3
Identify the linear graphs with a gradient of 3.
- $y=3x-3$ ✓
- $y=x+3$
- $y=7-3x$
- $y=3x+7$ ✓
- $y=11+3x$ ✓
These are all linear equations which give straight line graphs. Match each linear equation with another equation to form a pair of parallel lines.
- $y=5x-7$
  
  ⇔
  
  $y=5x+18$ ✓
- $y=3-2x$
  
  ⇔
  
  $y=-2x+7$ ✓
- $y=-4+2x$
  
  ⇔
  
  $y=2x-7$ ✓
- $y=7x-10$
  
  ⇔
  
  $y=7x$ ✓
- $y=7-x$
  
  ⇔
  
  $y=-2-x$ ✓
What features of the graph of $y=9x-15$ can be found just by looking at the equation?
- It is a straight line graph. ✓
- It has a gradient of $9$ ✓
- It has a gradient of $-15$
- It has a $y$ -intercept of $9$
- It has a $y$ -intercept of $-15$ ✓
Which of these equations could this sketch represent?
- $y=9x-15$ ✓
- $y=9x+15$
- $y=15-9x$
- $y=19x-156$ ✓
- $y=19x$

Worksheet

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Presentation

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Lesson Details

Key learning points

The gradient of the line is determined by m when the equation is in the form y = mx + c
The y-intercept is determined by c when the equation is in the form y = mx + c
You can sketch what the graph will look like from studying its equation

Common misconception

Estimation and approximation are only required skills when working solely with number problems.

In problem solving it can be really useful to sketch an approximation of a certain graph such as a linear equation. Seeing where the $y$ -intercept is and drawing an approximate gradient could help us identify solutions.

Keywords

Gradient - The gradient is a measure of how steep a line is.
Intercept - An intercept is the coordinate where a line or curve meets a given axis.
Linear - The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.