Y=mx+c

In this chapter we’re going to be looking at y=mx+c graphs. We shall explore the effects of m and c on the line in the y=mx+c equation. We shall then explore how to find the equation of a line drawn on a graph paper.

Example

Plot the graph of y=2x+1 To plot a graph we usually draw a table and then try to find the value of y for the chosen x values. You need to editing and make sure that the chosen values are close to each other, for example 1 to 10. Below is the table that will help us plot the graph of y=2x+1.

x y 0 1 1 3 2 5 3 7 4 9

Now we can plot these values on the graph as shown below. Now we join the plotted points with a single straight line.

M and C in y=mx+c In the equation y=mx+c m changes the steepness of the line. The following shows a graph which has lines whose m values have been changed.

The C in y=mx+c changes where the line intercepts the y-axis by moving it down or upwards. The following graph has lines whose C are different.

Gradient

Above we’ve seen that as the m value changes the steepness of the line changes. The steepness of the line in mathematics is known as gradient

We find the gradient on a straight line by dividing the number of units covered by a line across with the number of units covered by the line down. The following is the line of y=½x+c

One divided by two gives ½, this is what is known as the gradient of the line.

Finding the equation of a straight line Below we can see a graph whose equation is unknown.

Since the above is a straight line. The equation will be in the form of y=mx+c. We need to find the values of m and c in the equation. We know that the c value indicates where the line intercepts the y-axis so;

We know that m is the gradient of the line and we find this by dividing the upwards coverage with the downwards coverage;

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Math

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Remember to wrap math in $ ... $ or \[ ... \] to ensure proper formatting.

2 \times 3

2 \times 3

2^{34}

2^{34}

a_{i-1}

a_{i-1}

\frac{2}{3}

\frac{2}{3}

\sqrt{2}

\sqrt{2}

\sum_{i=1}^3

\sum_{i=1}^3

\sin \theta

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\boxed{123}

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Easy Math Editor

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Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$