Writing a linear equations

So (0, 1) is a point on the line and (1, 4) is a point on the line. To find the equation of the line, you use either

1) y = mx + c

2) y - y1 = m(x - x1)

1) is quicker if you know what c is (the y-intercept), 2) only needs one point on the line to find the equation if you know the gradient

and to find the gradient you divide the difference between two y coordinates by the different between two x coordinates, so the gradient is

m = (y2 - y1) / (x2 - x1)

So let's start:

Using points (0, 1) and (1, 4)

gradient m = (4 - 1) / (1 - 0) = 4

Now for the equation of the line,

1) using y = mx + c

You know that the line intercepts the y-axis at (0, 1), when y = 1, so c = 1.

We worked out the gradient m = 4

So using y = mx + c

y = 4x + 1

2) using y - y1 = m(x - x1)

You use any point on the line, (0, 1) is best because it has easy numbers.

Using the equation y - y1 = m(x - x1) and the point (0, 1) and the gradient m = 4, the equation of the line is

y - 1 = 4(x - 0)

y = 4x + 1