The equation in slope-intercept form for the line that passes through (1, -2) and (3, 7) is y = 4.5x - 6.5
To find the equation of a line in slope-intercept form, we need to use the formula:
y = mx + b
where m represents the slope and b represents the y-intercept.
First, let's calculate the slope (m):
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the given points (1, -2) and (3, 7) into the formula, we get:
m = (7 - (-2)) / (3 - 1) = 9 / 2 = 4.5
Next, we can substitute the slope and the coordinates of one of the points (1, -2) into the equation to find the y-intercept (b):
-2 = 4.5(1) + b
b = -2 - 4.5 = -6.5
Therefore, the equation in slope-intercept form for the line that passes through the points (1, -2) and (3, 7) is y = 4.5x - 6.5.