Final answer:
The equation of the line in standard form that passes through the points (2.5, -7) and (3, -8) is -2x + y = -2.
Step-by-step explanation:
To find the equation of the line that passes through the points (2.5, -7) and (3, -8) in standard form, we need to determine the slope and the y-intercept of the line.
Step 1: Calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (2.5, -7) and (3, -8):
m = (-8 - (-7)) / (3 - 2.5) = -1 / 0.5 = -2
Step 2: Substitute the slope and one of the points into the slope-intercept form (y = mx + b) to find the y-intercept (b). Using the point (2.5, -7):
-7 = -2(2.5) + b
-7 = -5 + b
b = -2
Step 3: Substitute the slope and y-intercept into the standard form equation (Ax + By = C).
-2x + y = -2
Therefore, the equation of the line in standard form that passes through the points (2.5, -7) and (3, -8) is -2x + y = -2.