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We want to find parallel lines to the given lines, such that also meet some given restrictions.
The solutions are:
A) y = 0.5*x - 6
B) two solutions:
y = 0.5*x + 4
y = 0.5*x
Before start answering, a general line is given by:
y = a*x + b
Where a is the slope and b is the y-intercept.
Another line will be parallel this if and only if it has the same slope and a different y-intercept.
A) We want to find a line that is parallel to y = 0.5*x + 10 and that intersects y = -1.5*x
So we want another line with a slope of 0.5, then the correct option is:
y = 0.5*x - 6
How do we know that this intercepts the other line?
Because if two lines have different slopes, then the lines are not parallel, meaning that at some given point the lines intercept.
B) Similarly, now we want a line parallel to:
y = 0.5*x + 10
And that intersects:
y = -1.5*x
The correct options are the ones with slope equal to 0.5, then we have two correct options:
y = 0.5*x + 4
y = 0.5*x
If you want to learn more, you can read:
https://brainly.com/question/16701300