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Chapter overview
Learning goals
Learning Goals
Maths
Types of numbers
Number calculations
Fractions, decimals and percentages
Algebraic manipulation
Formulae and equations
Straight line graphs
Other graphs
Ratio
Proportion
Rates of change
Shapes
Properties of shapes
Lines and angles
Drawing shapes
Trigonometry
Probability
Maths
Summary
The equation of a linear graph is $y=mx+c$. Given values of $m$ and $c$, this equation can be used to plot a straight line graph.
The gradient of a line is given by $m$. It indicates the steepness of the line and can be calculated with:
$m=\frac{\text{change in }y}{\text{change in }x}$
The $y$-intercept is given by $c$. This is the point on the $y$-axis where the line crosses.
One way to draw a straight line graph is to figure out two points that the line passes, before joining up those points and extending the line beyond them. Follow this procedure:
1. | The easiest point to start with is the $y$-intercept, given by $c$, since you know this is on the $y$-axis. Hence you have that the point $(0,c)$ is on the line. Mark this on the coordinate grid. |
2. | To find another point, simply pick an $x$-value (other than zero, since this will just give you the point you already have) and insert it into the equation of the line to find the corresponding $y$-coordinate. |
3. | Mark on this second point and join it up with the first point. |
A line has equation $y=3x-4$. Find the coordinates of two points on the line. Hence draw the line given by the equation.
Firstly, use the $y$-intercept $(x=0)$ to find the first point: $c=-4$
Point 1: $\underline{(0,-4)}$
Next, pick a non-zero $x$-value. In this instance, $x=1$. Insert this into the equation of the line:
$y=3x-4=3(1)-4=3-4=-1$
Point 2: $\underline{(1, -1)}$
Plot the two points found ($(0,-4)$ and $(1,-1)$) then join them up, extending beyond those points.
Not all linear graphs have the equation $y=mx+c$. Vertical lines have equations of the form $x=d$ where $d$ is a constant. These lines have the same $x$-coordinate all along the line, so are represented by a vertical line going through $x=d$ given a value of $d$.
Horizontal lines technically do have the form $y=mx+c$ but where $m=0$. These are just horizontal lines that go through $c$ on the $y$-axis.
The equation of a linear graph is $y=mx+c$. Given values of $m$ and $c$, this equation can be used to plot a straight line graph.
The gradient of a line is given by $m$. It indicates the steepness of the line and can be calculated with:
$m=\frac{\text{change in }y}{\text{change in }x}$
The $y$-intercept is given by $c$. This is the point on the $y$-axis where the line crosses.
One way to draw a straight line graph is to figure out two points that the line passes, before joining up those points and extending the line beyond them. Follow this procedure:
1. | The easiest point to start with is the $y$-intercept, given by $c$, since you know this is on the $y$-axis. Hence you have that the point $(0,c)$ is on the line. Mark this on the coordinate grid. |
2. | To find another point, simply pick an $x$-value (other than zero, since this will just give you the point you already have) and insert it into the equation of the line to find the corresponding $y$-coordinate. |
3. | Mark on this second point and join it up with the first point. |
A line has equation $y=3x-4$. Find the coordinates of two points on the line. Hence draw the line given by the equation.
Firstly, use the $y$-intercept $(x=0)$ to find the first point: $c=-4$
Point 1: $\underline{(0,-4)}$
Next, pick a non-zero $x$-value. In this instance, $x=1$. Insert this into the equation of the line:
$y=3x-4=3(1)-4=3-4=-1$
Point 2: $\underline{(1, -1)}$
Plot the two points found ($(0,-4)$ and $(1,-1)$) then join them up, extending beyond those points.
Not all linear graphs have the equation $y=mx+c$. Vertical lines have equations of the form $x=d$ where $d$ is a constant. These lines have the same $x$-coordinate all along the line, so are represented by a vertical line going through $x=d$ given a value of $d$.
Horizontal lines technically do have the form $y=mx+c$ but where $m=0$. These are just horizontal lines that go through $c$ on the $y$-axis.
FAQs
Question: What shape is a linear graph?
Answer: A linear graph is a straight line.
Question: What is a linear equation?
Answer: y=mx+c is a form of the linear equation. It gives a straight line when plotted.
Question: How do you use an equation of a line to find a point on the line?
Answer: Choose any x-coordinate and insert it into the equation of the line. This will give the y-coordinate. Hence you have the coordinates of a point on the line.
Question: How do you plot a linear graph from the equation?
Answer: Use the equation to locate two points on the line. Join these points up and extend the line beyond them.
Theory
Exercises
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