Final answer:
To rewrite the equations in slope-intercept form, the first one becomes y = ½x + 7.5, and the second one becomes y = ½x - 2.5. Since both have the same slope of ½, the lines are parallel.
Step-by-step explanation:
To rewrite the equations in slope-intercept form, we need to solve each equation for y. The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
For the first equation 2y = x + 15, let's divide both sides by 2 to isolate y:
y = ½x + ⅗×15
y = ½x + ⅗×(15)
y = ½x + 7.5
Now, let's rewrite the second equation x = 2y + 5 in slope-intercept form by subtracting 5 from both sides and then dividing by 2:
x - 5 = 2y
½(x - 5) = y
y = ½x - ½×5
y = ½x - 2.5
The two lines are parallel if their slopes are equal. The slope of both equations is ½, so the lines represented by these equations are indeed parallel.