Final answer:
The line parallel to the x-axis that passes through (5,4) has a slope of 0 and the equation in slope-intercept form is y = 4.
Step-by-step explanation:
The student has a question related to the slope of a line on a coordinate grid and writing the equation of that line in slope-intercept form.
a. Since the line is parallel to the x-axis and does not rise or fall as it moves along the x-axis, the slope of the line is 0. Slope (m) is calculated by the rise over run. In this case, there is no rise when you move along the line; hence the slope is 0.
b. With a slope of 0, the y-intercept determines where the line crosses the y-axis. Since the line passes through the point (5, 4), it never crosses the y-axis—it remains at y = 4 at all points along the line. Therefore, the equation of the line in slope-intercept form, which is y = mx + b, can be written as y = 4.