Question

1. what does a positive slope indicate about the direction of the line on a graph?

a. the line is horizontal
b. the line is vertical
c. the line rises from left to right
d. the line falls from left to right

1. what does y = mx + b represent in a system of linear equations?

a. the slope - intercept form of a line.
b. the elimination form of an equation.
c. the standard form of an equation.
d. the coefficient form of a quadratic equation.

1. if you solve a system of equations and both variables cancel out leaving a true statement like 0 = 0, what does it mean?

a. the system has exactly one solution.
b. the system has infinitely many solutions.
c. the equations are not linear.
d. the system has no solution.

Explanation:

• Question 6:
• A horizontal line has a slope of \(0\).
• A vertical line has an undefined slope.
• For a line with a positive slope, as \(x\) increases (from left to right on the graph), \(y\) also increases, so the line rises from left to right.
• A line with a negative slope falls from left to right.
• Question 7:
• The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.
• The elimination method is a way to solve a system of equations, not a form of an equation.
• The standard form of a linear equation is \(Ax + By=C\) (\(A\), \(B\), and \(C\) are constants, \(A\geq0\), \(A\) and \(B\) are not both zero).
• \(y = mx + b\) is a linear equation, not a quadratic equation (\(y=ax^{2}+bx + c,a

eq0\) is a quadratic equation).

• Question 8:
• If solving a system of equations results in a true statement like \(0 = 0\) (after the variables cancel out), it means that the two equations represent the same line.
• If a system has exactly one solution, the two lines intersect at a single point.
• If a system has no solution, the two lines are parallel.
• Just because we get \(0 = 0\) does not imply the equations are non - linear (we started with a system of equations, and if the process of solving (e.g., by substitution or elimination) leads to \(0 = 0\), the original equations are linear and coincident).

Answer:

• Question 6: C. The line rises from left to right
• Question 7: A. The slope - intercept form of a line
• Question 8: B. The system has infinitely many solutions