Question

question 7
an equation for a line in the plane allows you to find the x- and y-coordinates of any
point on that line.
a. true
b. false

question 8
a linear equation is an equation whose graph is a straight line.
a. true
b. false

question 9
the graph of a line goes up and to the right when:
a. there is no coefficient of x.
b. the coefficient of x is negative.
c. the coefficient of x is positive.
d. the coefficient of x is 0.

question 10
the equation $y = ax$ describes the graph of a line. if the value of a is negative, the line:
a. is horizontal.
b. goes down and to the left.
c. is vertical.
d. goes up and to the left.

Explanation:

• Question 7: A line's equation defines all (x,y) pairs on it, so given a value for one coordinate, the other can be calculated.
• Question 8: By definition, linear equations in two variables graph as straight lines.
• Question 9: The coefficient of x in a line's slope-intercept form ($y=mx+b$) is the slope $m$. A positive slope means the line rises as x increases (up and right).
• Question 10: In $y=ax$, $a$ is the slope. A negative slope means as x increases (moves right), y decreases (moves down); equivalently, as x decreases (moves left), y increases (moves up), so the line goes up and to the left.

Answer:

Question 7: A. True
Question 8: A. True
Question 9: C. the coefficient of x is positive.
Question 10: D. goes up and to the left.