Answer:
A, B, and C
Step-by-step explanation:
A) We can see if this is a horizontal line if its slope is 0. Slope is change in y divided by change in x, so: slope = [tex]\frac{7-7}{3-(-2)} =\frac{0}{5} =0[/tex] . Thus, this is a horizontal line and the statement is correct.
B) Any equation of the form x = k, where k is a constant, will always be a straight line. Let's see if it goes through (-8, 3) by plugging in the values of -8 in for x and 3 in for y in the equation.
Clearly, we don't have a y, so we just put in the -8 for the x: -8 = -8. Since this is a true statement, we know that x = -8 does go through (-8, 3). So, this is a true statement.
C) We can see if this is a vertical line if its slope is undefined (for example, if the denominator is 0, it's undefined). Slope = [tex]\frac{5-(-7)}{0-0} =\frac{12}{0}[/tex] = undefined. So, this is a vertical line and the statement is true.
D) As a basic fact, any point on a horizontal line will have the same y coordinate. However, their x coordinates may vary. Thus, the statement is false.
So, the answers are A, B, and C.
Hope this helps!
