Question

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Find the equation of the line. Use exact numbers

Answer 1

⇒ To find the equation of the straight line we have to first calculate the slope/gradient of the line .

• To calculate the slope of the line we need to have two points.
• From the question they say we must use exact points meaning we should only take points in the graph without decimals.
• I will take (4,1) and (8,4)

• Note you can take any two points of your choice as you would still reach to the same answer.

⇒To calculate the slope of the line you use the gradient formula below:

`m=(y_(2)-y_(1) )/(x_(2) -x_(1) ) \\`

⇒Calculating the slope of the line let us plug in the points of our choice from the graph and simplify.

`m=(4-1)/(8-4) \\m=(3)/(4\\) \\m=(3)/(4)`

⇒Note m is just a a letter of alphabet that represents the slope of the line.

⇒The slope of the line is
`(3)/(4)`

⇒ The general equation to calculate the straight line equation is

y=mx+c where y is the y coordinate

x is the x-coordinate

m is the slope

c is the y-intercept.

• The next step is to find the y-intercept of which is quite obvious in the picture at the graph that is -2 but to save you from doubts i will show you how we calculate is for future cases.

I will use any point (x,y) ,note you can use any point as you will still get the same value c

I will use the point (4,1) from the graph.

`1=4((3)/(4) )+c\\1=3+c\\1-3=c\\c=-2`

∴From the known values of the general equation

`y=(3)/(4) x-2` is our equation.