Find an equation of the line containing the given pair of points. Express your answer in the form x=a, y=b, or y = mx+b.
(0,0) and (5,4)
To find the equation of a line containing two points, we can use the point-slope form of a line. The point-slope form is given by y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) are the coordinates of one of the points on the line.
Let's find the slope first. The slope (m) is calculated as (change in y) / (change in x). Given the points (0, 0) and (5, 4), the change in y is 4 - 0 = 4 and the change in x is 5 - 0 = 5.
So, the slope is m = (4 - 0) / (5 - 0) = 4/5.
Now, let's use the point-slope form with the point (0, 0):
y - 0 = (4/5)(x - 0)
Simplifying, we have:
y = (4/5)x
Therefore, the equation of the line passing through the points (0, 0) and (5, 4) is y = (4/5)x.