complete the equation for the linear function whose graph contains the points (2,5) and (3,0)
y - ____ = _____(x -2) *fill in the blank
- not sure how to do this question
cleaning company charges a fee of $65 in addition to $10.50 per hour of cleaning.. x = the number of hours cleaning ; y = the total charge
y = ____x + ____ * fill in the blank
- not sure how to do this
What is an equation for the linear function whose graph contains the points (2, 5) and (3, 0)?
To complete the equation for the linear function, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Let's use the first point (2,5) to find the slope:
m = (y2 - y1) / (x2 - x1) = (0 - 5) / (3 - 2) = -5
Now we can substitute the values into the equation:
y - 5 = -5(x - 2)
Similarly, for the second question, we can use the given information to set up the equation.
The fee charged by the cleaning company is $65, which is a fixed amount regardless of the number of hours. This is represented by the y-intercept (0, $65) in the form (x, y).
The additional charge per hour of cleaning is $10.50. This is represented by the slope of the line.
So the equation for the linear function would be:
y = 10.50x + 65
To complete the equation for a linear function given two points, you need to find the slope (m) and the y-intercept (b) first.
1. Finding the slope (m):
The slope represents the rate of change of the function. It can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (2,5) and (3,0):
m = (0 - 5) / (3 - 2)
m = -5 / 1
m = -5
2. Finding the y-intercept (b):
The y-intercept is the value of y when x equals zero. To find the y-intercept, you can substitute one of the points into the slope-intercept form of a linear function, which is:
y = mx + b
Using the point (2,5):
5 = -5(2) + b
5 = -10 + b
b = 10 + 5
b = 15
Now you can complete the equations:
1. For the linear function:
Using the slope-intercept form, where m = slope and b = y-intercept:
y - y1 = m(x - x1)
Substituting the values (2,5) for (x1, y1):
y - 5 = -5(x - 2)
y - 5 = -5x + 10
y = -5x + 15
2. For the cleaning company charge:
Using the equation y = mx + b, where m represents the hourly rate and b represents the additional charge:
y = mx + b
Since the cleaning company charges $10.50 per hour and there is an additional fee of $65, the equation becomes:
y = 10.50x + 65
Thus, the completed equations are:
1. The linear function: y = -5x + 15
2. The cleaning company charge: y = 10.50x + 65
slope = (y-5)/(x-2) = (0-5)/(3-2) = -5/1
or
y - 5 = -5 (x-2)
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huh, it says the answer right in the sentence
y = 10.5 x + 65