Question

question 10 of 10
the graph of $y = -2x + 10$ is:

a. a line that shows only one solution to the equation.

b. a point that shows one solution to the equation.

c. a line that shows the set of all solutions to the equation.

d. a point that shows the $y$-intercept.

Explanation:

The equation \( y = -2x + 10 \) is in slope - intercept form (\( y=mx + b \)) of a linear equation. A linear equation in two variables has infinitely many solutions (pairs of \( x \) and \( y \) values that satisfy the equation). The graph of a linear equation in two variables is a straight line, and every point on this line represents a solution to the equation.

• Option A: A linear equation has infinitely many solutions, not just one, so this is incorrect.
• Option B: The graph of a linear equation is a line, not a single point, and it has infinitely many solutions, so this is incorrect.
• Option C: The graph of \( y=-2x + 10 \) is a line, and every point on the line is a solution to the equation, so it shows the set of all solutions. This is correct.
• Option D: The \( y \) - intercept is a point (\( (0,10) \) for this equation), but the graph of the equation is a line, not just the \( y \) - intercept point. So this is incorrect.

Answer:

C. a line that shows the set of all solutions to the equation.