Question

Kimberly measured the water level in her pool when it was raining heavily this summer. After 5 hours of rain, her pool had 58 inches of water. After 8 hours of rain, her pool was at 70 inches. Write an equation to show how many inches of water are in the pool after x hours have passed.

Write an equation in slope intercept form each

Answer 1

To find the equation showing the number of inches of water in the pool after x hours have passed, use the slope-intercept form. The equation is y = 4x + 38.

Step-by-step explanation:

To write an equation showing the number of inches of water in the pool after x hours have passed, we can use the concept of slope-intercept form. In slope-intercept form, the equation takes the form y = mx + b, where y represents the number of inches of water in the pool, x represents the number of hours that have passed, m represents the slope of the line, and b represents the y-intercept.

To find the equation, we first need to determine the slope (m) and the y-intercept (b) using the given data. We can use the two points (5, 58) and (8, 70) to find the values of m and b. Using the slope formula (m = (y2 - y1) / (x2 - x1)), we have m = (70 - 58) / (8 - 5) = 4. Next, we can substitute the values of one of the points, such as (5, 58), into the equation and solve for b. Since y = mx + b, we have 58 = 4(5) + b, which simplifies to 58 = 20 + b. Solving for b, we find that b = 38.

Therefore, the equation showing the number of inches of water in the pool after x hours have passed is y = 4x + 38.