Question

Graph the line that passes through the points (5, 0) and (9, 4) and determine the equation of the line.

Answer 1

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.