Question

question 7 (multiple choice worth 2 points)
(solve systems of equations by graphing mc)

graph the system of equations.

3x - y = 2

y + 4 = 3(x + 4)

Explanation:

Step1: Rewrite equations in slope - intercept form

For the first equation \(3x - y=2\), we can rewrite it as \(y = 3x-2\). The slope \(m_1 = 3\) and the y - intercept \(b_1=- 2\).
For the second equation \(y + 4=3(x + 4)\), expand the right - hand side: \(y+4 = 3x+12\). Then, subtract 4 from both sides to get \(y=3x + 8\). The slope \(m_2 = 3\) and the y - intercept \(b_2 = 8\).

Step2: Analyze the lines

Since the slopes of the two lines \(m_1=m_2 = 3\) and the y - intercepts \(b_1
eq b_2\) (\(-2
eq8\)), the two lines are parallel. When graphing, we can plot the y - intercepts first. For \(y = 3x-2\), plot the point \((0,-2)\), and for \(y=3x + 8\), plot the point \((0,8)\). Then, using the slope (rise over run, since slope \(m = 3=\frac{3}{1}\), for each 1 unit we move to the right along the x - axis, we move up 3 units along the y - axis), we can draw the two lines. The two lines will never intersect because they are parallel (same slope, different y - intercepts).

Answer:

The two lines \(y = 3x-2\) (from \(3x - y = 2\)) and \(y=3x + 8\) (from \(y + 4=3(x + 4)\)) are parallel. When graphing, one line passes through \((0,-2)\) with a slope of 3, and the other passes through \((0,8)\) with a slope of 3, and they do not intersect.