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Straight Line Graphs 3

Straight Line Graphs 3

Straight Line Graphs 3

We can identify the gradient and y-intercept if we are given a set of coordinates which feature on a line.

The gradient can be found by using a formula with coordinates located on a line.


Find the gradient of the line joining (3,4)(3,4) and (5,6)(5, 6)

Let's find the equation of a line when we do not know the y-intercept.

For example, let's find the equation of the line joining (6,20)(6,20) and (4,14)(4,14)


We can't immediately see the y-intercept

Neither of the points have an xx value of 0, so neither of them are the point at which the line crosses the y-axis.


Start by finding the gradient

Remember the formula: difference in ydifference in x\dfrac{difference \space in\space y}{difference \space in \space x}


What is the gradient between these points?


Substitute the gradient into the equation

Now we have a value for mm, we can put this into an equation containing one of the points. Remember, the coordinates contain the x and y values at that point.


Let's do this for the point (4,14)(4,14)

For y=mx+cy=mx+c, 14=3(4)+c14=3(4)+{\color{#21affb}c}. We can rearrange this to find cc.


Subtract 12 from both sides

1412=12+c  c=214-12={\cancel{12}}+ c \space \rightarrow\space c=2


Nice! 😎

Now we know mm and cc, we can see that our equation is y=3x+2y=3x+2. You can check this by substituting in the values of the other point.