Lesson HOW TO find equations, slopes and intercepts of straight lines

Source code of 'HOW TO find equations, slopes and intercepts of straight lines'

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About longjonsilver: I have a new job in September, teaching

There are only a few types of questions that we can ask to test your knowledge of straight lines and coordinates. Here they are:

1. Find the equation of the line given 2 points

EXAMPLE:

<BLOCKQUOTE>Given points (-1,4) and (2,13), find the equation of the straight line that passes through them.</BLOCKQUOTE>

solution:
We know the equation will be of the form y=mx+c, so we just need to find the gradient, m and the y-intercept, c. These are simple enough exercises.

Gradient, m = {{{(y2-y1)/(x2-x1)}}}

m = {{{(13-4)/(2-(-1))}}}
m = 9/3
m=3

so, we have y=3x+c now.

To find c, we need to know x and y. Well, we do. We know 2 sets of x and y...the coordinates in the question, so just pick one pair and put them in the equation to find c...I will choose (-1,4):

4 = 3(-1) + c
4 = -3 + c
--> c = 7

so the equation is y=3x + 7.

Check now with your other pair of coordinates. Put the x-value in and see if the y-value you calculate matches that in the question:

when x=2, y=3(2) + 7, so y=6+7 ie y=13, which is correct. So we KNOW the answer is correct.

2. Find the equation of the line given 1 point and the gradient

EXAMPLE:

<BLOCKQUOTE>Find the equation of the straight line that passes through point (3,4) and has a gradient of -5.</BLOCKQUOTE>

solution:
This is a lot simpler than the previous example, since we already know the gradient - no need to calculate it.

Starting with y=mx+c, put in the information we know, namely, x,y and m...

4 = -5(3) + c
4 = -15 + c

--> c = 19

so the equation is y=-5x+19

3. Find the gradient and y-intercept of a given straight line

EXAMPLE:
<Blockquote>Find the gradient and y-intercept of the equation 3y + 12x - 7 = 0.</Blockquote>

solution:

We need the equation in the y=mx+c form, so we need to re-arrange it.

3y + 12x - 7 = 0 --> add 7 to both sides
3y + 12x = 7 --> subtract 12x from both sides
3y = -12x + 7 --> now divide everything by 3
{{{y = -4x + 7/3}}}

This is the same equation, but in the correct form, to tell us the gradient and y-intercept, ie

gradient = -4
y-intercept = 7/3