1. To find the equation that shows the relationship between x and y, we can examine the data provided. We notice that when x is equal to 8, y is equal to 40. Similarly, when x is equal to 5, y is equal to 25. We can assume that there is a linear relationship between x and y.
To find the equation of this line, we can use the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
First, we need to find the slope (m) using two points (8, 40) and (5, 25):
m = (y2 - y1) / (x2 - x1)
m = (25 - 40) / (5 - 8)
m = -15 / -3
m = 5
Now, we can find the y-intercept (b) by substituting the slope and one of the points into the equation:
y = mx + b
25 = 5(5) + b
25 = 25 + b
b = 0
So, the equation that shows the relationship between x and y is y = 5x.
2. The relationship is A. proportional because the equation y = 5x represents a straight line passing through the origin (0, 0). The y-intercept is 0, indicating that when x is 0, y is also 0. This indicates a proportional relationship where the ratio between x and y is constant.
given table for x, time in minutes and y, distance traveled in meter
x - time (minutes) | 8 | 5 | 7 | 2 | 9 |
y - distance (meters) | 40 | 25 | 35 | 10 | 45 |
1. write an equation to show the relationship between x and y ______
2. The relationship is ______ because the y-intercept is _____
A. proportional
B. non proportional
C. non linear
1 answer