The pair of points lies on the same line with the given slope. Find x.
(4, 4), (x, 10); slope = 2
The formula for finding the slope between two points is:
slope = (y2 - y1)/(x2 - x1)
Using the given points (4, 4) and (x, 10), we can substitute these values into the formula to solve for x:
2 = (10 - 4)/(x - 4)
To solve for x, we can cross multiply:
2(x - 4) = 10 - 4
2x - 8 = 6
Adding 8 to both sides:
2x = 14
Dividing both sides by 2:
x = 7
So, x = 7.
The following table contains ordered pair solutions of a linear equation in two variables. Use the table to find the slope of the graph.
x = -3, 1, -6
y = -7, 1, -13
To find the slope of the graph using the given table of ordered pairs, we can use the formula:
slope = (change in y)/(change in x)
Let's use the first two points (-3, -7) and (1, 1) to calculate the slope:
change in y = 1 - (-7) = 1 + 7 = 8
change in x = 1 - (-3) = 1 + 3 = 4
slope = (8)/(4) = 2
Therefore, the slope of the graph is 2.
Without graphing, tell whether the slope of a line that models the linear relationship is positive, negative, zero, or undefined. Then find the slope.
A laptop battery has 81% power left after 1 hour of use and 43% after 3 hours of use
To determine the slope of a line modeling the linear relationship between the hours of use and the percentage of battery power remaining, we can calculate the change in percentage of power divided by the change in hours.
change in percentage of power = 43% - 81% = -38%
change in hours of use = 3 hours - 1 hour = 2 hours
slope = (change in percentage of power)/(change in hours of use)
= (-38%)/(2 hours)
= -19%
Therefore, the slope of the line modeling the linear relationship is negative.
To find the value of x when the pair of points lies on the same line with the given slope, we can use the formula for slope:
slope = (y2 - y1) / (x2 - x1)
We are given the slope as 2, and the coordinates of the two points as (4, 4) and (x, 10). Using the formula, we can plug in the values to the equation:
2 = (10 - 4) / (x - 4)
Next, we can simplify the equation:
2 = 6 / (x - 4)
To get rid of the fraction, we can cross multiply:
2(x - 4) = 6
Distribute the 2 on the left side:
2x - 8 = 6
Add 8 to both sides of the equation:
2x = 14
Finally, divide both sides by 2:
x = 7
Therefore, the value of x is 7.