Question
Suppose that the water level of a river is 45 feet after 3 days of no rain and 10 feet after 10 days of no rain. Given the two points we know: (3, 45) and (10, 10), what would the point slope equation look like?
Answers
Answered by
GPT 3.5
To find the point-slope equation, we need to calculate the slope between the two given points. The formula for slope (m) is:
m = (y2 - y1) / (x2 - x1)
Using the points (3, 45) and (10, 10):
m = (10 - 45) / (10 - 3)
m = -35 / 7
m = -5
Now that we have the slope, we can use one of the points (3, 45) along with the slope in the point-slope form equation:
y - y1 = m(x - x1)
Using (3, 45):
y - 45 = -5(x - 3)
This is the point-slope equation.
m = (y2 - y1) / (x2 - x1)
Using the points (3, 45) and (10, 10):
m = (10 - 45) / (10 - 3)
m = -35 / 7
m = -5
Now that we have the slope, we can use one of the points (3, 45) along with the slope in the point-slope form equation:
y - y1 = m(x - x1)
Using (3, 45):
y - 45 = -5(x - 3)
This is the point-slope equation.
Answer
What would the y intercept be
Answered by
GPT 3.5
To find the y-intercept, we can substitute the coordinates of one of the given points into the equation we found in the previous step. Let's use the point (3, 45):
y - 45 = -5(x - 3)
Substituting 3 for x and 45 for y:
45 - 45 = -5(3 - 3)
0 = 0
Therefore, the y-intercept is 0. The equation can be simplified to:
y = -5x + 45
y - 45 = -5(x - 3)
Substituting 3 for x and 45 for y:
45 - 45 = -5(3 - 3)
0 = 0
Therefore, the y-intercept is 0. The equation can be simplified to:
y = -5x + 45
Answer
That is not a option
Answered by
GPT 3.5
Apologies for the incorrect response. Let's recalculate the y-intercept using the given points.
Using the point-slope equation:
y - 45 = -5(x - 3)
Let's substitute the coordinates from one of the points, such as (3, 45):
45 - 45 = -5(3 - 3)
0 = 0
Since 0 = 0, it means that the equation is satisfied for any value of x. Therefore, there is no specific y-intercept in this case. Instead, the line defined by the two given points is horizontal.
Using the point-slope equation:
y - 45 = -5(x - 3)
Let's substitute the coordinates from one of the points, such as (3, 45):
45 - 45 = -5(3 - 3)
0 = 0
Since 0 = 0, it means that the equation is satisfied for any value of x. Therefore, there is no specific y-intercept in this case. Instead, the line defined by the two given points is horizontal.
Answer
That is also not right
Answered by
GPT 3.5
Apologies for the previous incorrect responses. Let's recalculate the y-intercept using the correct information.
Given the points (3, 45) and (10, 10), we can use the point-slope form equation:
y - y1 = m(x - x1)
Using the point (3, 45) and the slope we calculated earlier (-5):
y - 45 = -5(x - 3)
Expanding the equation:
y - 45 = -5x + 15
Now we can rearrange the equation to slope-intercept form (y = mx + b), where b represents the y-intercept:
y = -5x + 15 + 45
y = -5x + 60
So the point-slope equation in slope-intercept form is y = -5x + 60, where the y-intercept is 60.
Given the points (3, 45) and (10, 10), we can use the point-slope form equation:
y - y1 = m(x - x1)
Using the point (3, 45) and the slope we calculated earlier (-5):
y - 45 = -5(x - 3)
Expanding the equation:
y - 45 = -5x + 15
Now we can rearrange the equation to slope-intercept form (y = mx + b), where b represents the y-intercept:
y = -5x + 15 + 45
y = -5x + 60
So the point-slope equation in slope-intercept form is y = -5x + 60, where the y-intercept is 60.
Answer
What would the equation for the acne Rio in slope intercept be
Answered by
GPT 3.5
Apologies for the confusion. Let's find the equation of the line in slope-intercept form given the points (3, 45) and (10, 10).
First, calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (3, 45) and (10, 10):
m = (10 - 45) / (10 - 3)
m = -35 / 7
m = -5
Now, we have the slope, we can use the slope-intercept form of a linear equation:
y = mx + b
Where m is the slope and b is the y-intercept.
To find the y-intercept, we can substitute one of the points into the equation. Let's use (3, 45):
45 = -5(3) + b
45 = -15 + b
b = 60
Therefore, the equation for the line in slope-intercept form is:
y = -5x + 60.
First, calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (3, 45) and (10, 10):
m = (10 - 45) / (10 - 3)
m = -35 / 7
m = -5
Now, we have the slope, we can use the slope-intercept form of a linear equation:
y = mx + b
Where m is the slope and b is the y-intercept.
To find the y-intercept, we can substitute one of the points into the equation. Let's use (3, 45):
45 = -5(3) + b
45 = -15 + b
b = 60
Therefore, the equation for the line in slope-intercept form is:
y = -5x + 60.