Let's start by defining the two points we are working with, which are point1(3, 0) and point2(5, 2).
The first thing we have to do to find the equation of a line in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, is to calculate m, the slope of the line, using the formula m = (y2 - y1) / (x2 - x1).
In this case, point1 is (x1, y1) and point2 is (x2, y2), so using the values we have:
m = (2 - 0) / (5 - 3) = 2 / 2 = 1
So, the slope of the line is 1.
The next step is to find b, the y-intercept. The y-intercept is the point at which the line crosses the y-axis. We calculate this knowing the slope and one point on the line, for this, we can use either point1 or point2.
The formula to find the y-intercept (b) is: b = y - mx.
Using point1(3, 0) and our calculated slope(m = 1) we get:
b = 0 - 1*3 = -3
So the y-intercept of the line is -3.
Finally, we can write down the equation of the line in slope-intercept form using the calculated slope and y-intercept:
The equation is: y = 1x - 3 or simply y = x - 3.