Graph the line that passes through the points (5, 0) and (9, 4) and determine the equation of the line.
To find the equation of the line that passes through the points (5, 0) and (9, 4), we need to find the slope of the line and its y-intercept.
First, let's find the slope.
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1)/(x2 - x1)
Using (x1, y1) = (5, 0) and (x2, y2) = (9, 4), we can substitute the values into the slope formula:
slope = (4 - 0)/(9 - 5) = 4/4 = 1
Next, let's find the y-intercept.
For a line in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept, we can substitute one of the points into the equation to solve for b.
Using the point (5, 0):
0 = 1(5) + b
0 = 5 + b
b = -5
Now, we have the slope (m = 1) and the y-intercept (b = -5), we can write the equation of the line:
y = 1x - 5
y = x - 5
Therefore, the equation of the line that passes through the points (5, 0) and (9, 4) is y = x - 5.