Question

Question

Use the image to answer the question.

A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The equation of the solid line is y equals negative x plus 3. The equation of the dashed line is x plus y equals 8.

Solving the system y=−x+3
and x+y=8
by graphing shows that there is no solution to the system. Is this statement true or false? Explain.

(1 point)
Responses

The statement is true, because the lines have an intersection point.
The statement is true, because the lines have an intersection point.

The statement is true, because the lines are parallel.
The statement is true, because the lines are parallel.

The statement is false, because the lines are parallel.
The statement is false, because the lines are parallel.

The statement is false, because the lines have an intersection point.

Answer 1

The statement is true, because the lines are parallel.

To explain, let's look at the equations of the lines:

1. The equation of the solid line is \( y = -x + 3 \). This line has a slope of -1.
2. The equation of the dashed line is \( x + y = 8 \), which can be rewritten as \( y = -x + 8 \). This line also has a slope of -1.

Both lines have the same slope (-1) but different y-intercepts (3 for the solid line and 8 for the dashed line). Since parallel lines do not intersect, there is no solution to the system of equations. Therefore, the statement provided is true.