How do I put the points 0 0.5 and 3 499.5 in y equals a plus bx format?

Answer 1

If you know the slope (m) of a line and a point (X, Y) on that line you can use the formula for a line in the format:

y - Y = m(x - X)

But this can be rearranged to give:

y = mx - mX + Y

→ y = (Y - mX) + mx

→ y = a + bx

where a = Y - mX

and b = m

The slope of a line between two points (x0, y0) and (x1, y1) is given by:

slope = change_in_y / change_in_x

→ m = (y1 - y0) / (x1 - x0)

So for the points (0, 0.5) and (3, 499.5) this gives:

m = (499.5 - 0.5) / (3 - 0) = 499/3 = 166 1/3

Using (0, 0.5) as the point (X, Y), this gives:

a = 0.5 - 0 × 166 1/3 = 0.5

b = 166 1/3 =166.333... ≈ 166.33

→ the line between (0, 0.5) and (3, 499.5) has equation

y = 0.5 + 166 1/3 x

or

y = 0.5 + 166.333... x

which gives

y ≈ 0.5 + 166.33x

Answer 2

y = 0.5 + 166.33... *x