Final answer:
The line passing through the points (0, 2) and (5, 2) is horizontal with a slope of 0, making the correct equation y = 2.
Step-by-step explanation:
To find the equation of the line that passes through the points (0, 2) and (5, 2), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. The slope (m) is defined as the rise divided by the run.
Since the y-coordinates are the same for both points, the rise is 0, which means the slope is 0, indicating a horizontal line. The y-intercept (b) is the value of y when x is 0, which is given as 2 in the first point (0, 2).To find the line that passes through the points (0, 2) and (5, 2), we need to determine the equation using the point-slope form: y - y1 = m(x - x1), where (x1, y1) is one of the given points and m is the slope.
First, let's calculate the slope: m = (y2 - y1) / (x2 - x1) = (2 - 2) / (5 - 0) = 0 / 5 = 0.
Since the slope is 0, the equation of the line will only have a y-intercept. So the equation is y = 2. The correct answer is option d) y = 2.
Therefore, the equation of our line is y = 2, which is a horizontal line that crosses the y-axis at 2. Hence, the correct option is d) y = 2.