What is the distance between two points with x-coordinates 4 and 8 on the straight line with the equation y=(3/4)x-2

Firstly, to be able to find the distance between the two points we must find the y-coordinates of each point by substituting in the x values. For x=4y=3/4x4-2=1For x=8y=3/4x8-2=4Now that we know the coordinates of the points, we can find the distance between them. If we imagine a line drawn 4 units across from the first point (4,1) and then up 3 units form there to the second point (8,4) we can see the problem as a right-angled triangle with sides of distance 3 and 4. For the triangle we can use Pythagoras' theorem of a^2+b^2=c^2 to find the distance between the two points, c. If we rearrange the equation to make c the subject we get c=(a^2+b^2)^(1/2)Therefore, c=(3^2+4^2)^(1/2)c=(9+16)^(1/2)c=25^(1/2)c=5So the distance between the 2 points is 5 units