19. Which statement describes the relationship between the line graphs of the equations below?
y=-2x+4
y=0.5x+4
A.The line graph are the same line.
B.The line graph are parallel lines.
C.The line graph are perpendicular lines.
D.The line graphs intersect, but are not perpendicular.
E. Can't determine
I think the answer is choice C.
-2 = -1/.5
so they are perpendicular, yes, C
To determine the relationship between the line graphs of the equations y = -2x + 4 and y = 0.5x + 4, we need to compare their slopes.
For the first equation, y = -2x + 4, the slope is -2. This means that for every 1 unit increase in x, the y-coordinate decreases by 2 units.
For the second equation, y = 0.5x + 4, the slope is 0.5. This means that for every 1 unit increase in x, the y-coordinate increases by 0.5 units.
Since the slopes are different, the line graphs of the two equations cannot be the same line or parallel lines. We can eliminate options A and B.
To determine if the line graphs are perpendicular or intersecting, we need to compare the product of their slopes. If the product is -1, then the lines are perpendicular. If the product is not -1, then the lines intersect but are not perpendicular.
The product of -2 (slope of the first equation) and 0.5 (slope of the second equation) is -1. This means that the line graphs are perpendicular. Therefore, the correct answer is option C: The line graphs are perpendicular lines.