Question

Which statements are true? Check all that apply.

Answer 1

Answer:

-The line that goes through the points (3,7) and (–2,7) is a horizontal line.

-The equation x = –8 is a vertical line that goes through the point (–8,3).

-The line that goes through the points (0,5) and (0,–7) is a vertical line.

Step-by-step explanation:

-The line that goes through the points (3,7) and (–2,7) is a horizontal line.

The equation of this line is y = 7

-The equation x = –8 is a vertical line that goes through the point (–8,3).

The equation of this line is x = -8

-The line that goes through the points (0,5) and (0,–7) is a vertical line.

The equation of this line is x = 0

-The points on a horizontal line have the same x-coordinate.

Same x-coordinate is on a vertical line, not horizontal

Answer 2

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 = $\frac{7-7}{3-(-2)} =\frac{0}{5} =0$ . 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 = $\frac{5-(-7)}{0-0} =\frac{12}{0}$ = 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!