The measure of 1 = x + 8 and the measure of 7 = 3x - 20. What value of x will show that lines f and g are parallel?
To show that lines f and g are parallel, we need to determine if the slopes of the lines are equal. In order to find the slopes of lines f and g, we need to find the values of x that make the given equations true.
Given:
The measure of 1 = x + 8
The measure of 7 = 3x - 20
We can rewrite these equations to find the values of x:
1 = x + 8 => x = 1 - 8 = -7
7 = 3x - 20 => 3x = 7 + 20 = 27 => x = 27/3 = 9
Now we have found two values of x: x = -7 and x = 9.
To determine if lines f and g are parallel, we need to check if the slopes of the lines are equal. The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
For line f, we use the equation 1 = x + 8. Since the coefficient of x is 1, the slope of line f is 1.
For line g, we use the equation 7 = 3x - 20. Since the coefficient of x is 3, the slope of line g is 3.
Therefore, the slopes of lines f and g are different (1 for f and 3 for g). Hence, the lines f and g are not parallel.
To show that lines f and g are parallel, we need to find the value of x that makes the slopes of the two lines equal.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
The given equations are:
1 = x + 8 ...(1)
7 = 3x - 20 ...(2)
To find the slope of line f, we can rewrite equation (1) in slope-intercept form:
1 = x + 8
Simplifying, we have:
x = -7
So, the equation of line f can be written as:
f: y = x + 8
To find the slope of line g, we can rewrite equation (2) in slope-intercept form:
7 = 3x - 20
Adding 20 to both sides, we have:
27 = 3x
Dividing by 3, we get:
x = 9
So, the equation of line g can be written as:
g: y = 3x - 20
Now, let's compare the slopes of lines f and g:
The slope of line f is 1, as the coefficient of x is 1.
The slope of line g is 3, as the coefficient of x is 3.
To make the slopes of lines f and g equal, we need to find the value of x that makes 1 equal to 3. However, this is not possible since 1 will never be equal to 3, regardless of the value of x.
Therefore, there is no value of x that will make lines f and g parallel.