The measure of 2 = 2x + 12 and the measure of 8 = 4x - 48. What value of x will show that lines f and g are parallel?
What are f and g?
The question makes no sense to me as stated.
What you have written are two equations. I have no idea what "measure" you are talking about.
The equations can be rewritten
2x = -10 and 4x = 56
They lead to x = -5 and x = 14. On a graph, they are both vertical lines.
To determine which value of x will show that lines f and g are parallel, we need to compare the slopes of the two lines. Parallel lines have equal slopes.
Given that the measure of 2 is equal to 2x + 12 and the measure of 8 is equal to 4x - 48, we can find the slopes of lines f and g by converting the equations to the slope-intercept form (y = mx + b), where m represents the slope.
The measure of 2: 2 = 2x + 12
Rearrange the equation to isolate y:
2x + y = 2 + 12
y = -2x + 14
The measure of 8: 8 = 4x - 48
Rearrange the equation to isolate y:
4x - y = 8 + 48
y = 4x - 56
Now we have the equations of the lines f and g in slope-intercept form:
f: y = -2x + 14
g: y = 4x - 56
Comparing the slopes, we can see that the slope of line f is -2, and the slope of line g is 4. Since the slopes are not equal, lines f and g are not parallel for any value of x.