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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).

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Have a Free Meeting with one of our hand picked tutors from the UK’s top universities

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