Consider the given equation of a line.
y= 0.5x-10
When lines are parallel, they have the same slope. With this, we know that all lines that are parallel to our given line will have the same slope of 0.5= 12. Knowing this, we can write a general equation in slope-intercept form for all the lines parallel to the given line.
y= 0.5x+ b
On the other hand, since we are not asked for a line that passes through a particular point, we can choose any value for b. If we arbitrarily choose b= - 6, we get the following equation.
y= 0.5x -6
Just to see that their graphs are parallel, let's plot them using the slope and the y-intercept of each line.
Note that since b can be any real number other than -10, there are infinitely many solutions to this exercise. Here we have shown just one possibility.
