Heath was climbing a mountain. 3 hours after he began climbing, he was at an altitude of 600 feet. After 5 hours, he is at an altitude of 900 feet.
Which equation shows the relationship between y, Heath’s altitude, and x, the number of hours he has been climbing?
Heath was climbing a mountain. 3 hours after he began climbing, he was at an altitude of 600 feet. After 5 hours, he is at an altitude of 900 feet.
Which equation shows the relationship between y, Heath’s altitude, and x, the number of hours he has been climbing?
y-600=300(x-3)
y-600=150(x-3)
y+600=300(x+3)
y+600=150(x+3)
The correct equation is y-600=300(x-3). This equation represents the change in altitude (y-600) as a function of the number of hours climbing (x-3), with a rate of change of 300 feet per hour.
The correct equation that shows the relationship between y, Heath's altitude, and x, the number of hours he has been climbing is:
y - 600 = 300(x - 3)
To find the equation that shows the relationship between Heath's altitude (y) and the number of hours he has been climbing (x), we need to consider the given information.
We are told that after 3 hours, Heath was at an altitude of 600 feet, and after 5 hours, he was at an altitude of 900 feet.
Given these two data points, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the slope (m), we can use the formula: m = (change in y) / (change in x). In this case, the change in y is 900 - 600 = 300, and the change in x is 5 - 3 = 2. Therefore, the slope (m) is 300 / 2 = 150.
Now, let's substitute one of the data points into the equation y = mx + b. Let's use the point (3, 600), which represents the altitude after 3 hours. Substituting the values into the equation, we get:
600 = 150(3) + b
600 = 450 + b
b = 600 - 450
b = 150
Now we know the slope (m = 150) and the y-intercept (b = 150). Putting it all together, the equation that represents the relationship between y and x is:
y = 150x + 150
Therefore, the correct equation that shows the relationship between Heath's altitude (y) and the number of hours he has been climbing (x) is y = 150x + 150.