Question

1. the lines $2x - y = -3$ and $y = \frac{1}{2}x + 3$ are shown on the graph.

which statement about these lines is true?

Explanation:

Step1: Rewrite the first equation

Rewrite \(2x - y=-3\) in slope - intercept form (\(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept).
We can solve for \(y\):
\(2x - y=-3\)
Subtract \(2x\) from both sides: \(-y=-2x - 3\)
Multiply both sides by \(- 1\): \(y = 2x+3\)

Step2: Analyze the slopes and y - intercepts

For the line \(y = 2x + 3\), the slope \(m_1=2\) and the y - intercept \(b_1 = 3\).
For the line \(y=\frac{1}{2}x + 3\), the slope \(m_2=\frac{1}{2}\) and the y - intercept \(b_2 = 3\).

Since \(b_1=b_2 = 3\), the two lines have the same y - intercept, which means they intersect at the y - axis (at the point \((0,3)\)). Also, since \(m_1
eq m_2\) ( \(2
eq\frac{1}{2}\)), the lines are not parallel (parallel lines have equal slopes) and they intersect at one point (the point with the same y - intercept, \((0,3)\) in this case).

(Note: Since the actual options for the "Which statement..." are not provided, we can infer the true statement based on the equations. If the options were about intersection, slopes, or y - intercepts, the true statement would be related to the fact that they have the same y - intercept (so they intersect at \((0,3)\)) and different slopes (so they are not parallel). For example, if an option was "The lines intersect at the point \((0,3)\)" or "The lines have the same y - intercept", that would be the true statement.)

Answer:

(Assuming the options include a statement about the lines having the same y - intercept or intersecting at \((0,3)\), for example, if the options are:
A. The lines are parallel.
B. The lines have the same y - intercept.
C. The lines have the same slope.
D. The lines do not intersect.

Then the answer is B. The lines have the same y - intercept.)