Write the equation of a line in slope intercept form that passes through (2,4) and (5,4).
slope = m = (4-4)/(5-2 ) = 0 of course
when x = 0, y = 4
in fact when x = anything y = 4 because this is a horizontal line
y = 0 x + 4
or really y = 4
To write the equation of a line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b).
The slope (m) of a line can be calculated using the formula:
m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line.
Given the two points (2,4) and (5,4), we can substitute the coordinates into the formula to find the slope:
m = (4 - 4) / (5 - 2) = 0 / 3 = 0
Since the y-coordinate of both points is 4, the line is parallel to the x-axis, making the slope 0.
Now, we can substitute the slope (m = 0) and one of the points (5,4) into the slope-intercept form (y = mx + b) to determine the y-intercept (b):
4 = 0 * 5 + b
4 = b
Since the value of b is 4, the equation of the line in slope-intercept form is:
y = 0x + 4
y = 4