If two points on a graph are (-2,5) and (3,5), determine the equation of the line in slope-intercept form.

Answer 1

To determine the equation of a line in slope-intercept form, you need to find the slope and the y-intercept of the line.

The slope (m) of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
m = (y2 - y1)/(x2 - x1)

Applying this formula to the given points (-2,5) and (3,5),
m = (5 - 5)/(3 - (-2))
m = 0/5
m = 0

The line passing through these two points is a horizontal line, meaning that the slope is zero.

The y-intercept of a line is the value of y when x equals zero. Since the given points (-2,5) and (3,5) lie on a horizontal line with y = 5, the y-intercept will be 5.

Therefore, the equation of the line in slope-intercept form is:
y = mx + b
y = 0x + 5
y = 5