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Find the equation of the straight line which passes through the points (5, 0) and (6, 4).

We can use the general equation of a straight line to tackle this question: y=mx+c (m is the gradient and c is the y-intercept).(Note: The points are in the form (x, y).)
First, we will determine the gradient 'm'.
The gradient is another term for a slope, it determines how inclined the line joining two points is.To find out the value of the gradient, we need to calculate the ratio of the difference between the y values and the difference between the x values. The formula for this is m=(y1-y2)/(x1-x2).
In this case, we will take (5, 0) as the first point and (6, 4) as the second point. (i.e. x1 = 5, y1 = 0, x2 = 6, y2 = 4).So the gradient will be m = (0-4)/(5-6) = -4/-1 = 4.(Note: It doesn't matter which point we take as the first point and which point we take as the second point, as long as we are consistent in both the x and y values.)
Now that we have the gradient, we need to determine the value of the y-intercept 'c'.
To do this, we chose one of the points given to us. Let's say we choose (5, 0).We need to plug it into the generic equation y=mx+c with our calculated m value to get a value for c. (The value for c will be the same for any point on the line, so we can choose to use either of the points given to us in the question).
So with m=4, y=0 and x=5, we have0=(4)(5)+c0=20+cc=-20
This yields us out constant (unchanging no matter the coordinates) value of c as -20.
So our equation for this particular line is y=4x-20.
This is the solution to the question. We can now use this to determine any y value when we are given an x value, and to determine any x value when we are given a y value.
For example, if we were asked to find the y coordinate on this line where x=1,we would havey = 4(1)-20 = 4-20 = -16.
So our full coordinate would be (1, -16).

Answered by Chloe M. Maths tutor

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Answered by Chloe M.
Maths tutor

163 Views

See similar Maths GCSE tutors