6-3/4x+1/3=1/2x+5
6+1/3-5=1/2x+3/4x
4/3=5/4x
x=16/15
Answer: Any line with a slope of 4/7 and a y-intercept that is NOT -2
You should first turn the equation into y intercept form:
7y - 4x = -14; Add 4x from both sides
7y = 4x - 14; divide 7 from both sides
y = 4/7x - 2
Since you did not include choices, the answer will be the line with the slope 4/7 and without the y-intercept -2, because lines that are parallel will always have the same slope.
Example Answers: y = 4/7x + 2, y= 4/7x - 4
y = 4/7x + 10
Remark
You can just look at the graph to find out the y intercept. The y intercept is the point where x = 0. The point for the y intercept is (0,-2). So B is definitely wrong.
To get the slope, you can just use the x intercept which is (-3,0)
When y = 0, x = - 3. We need to do a little calculation to get the slope.
So far what we have is
y = mx - 2
y = 0
x = -3
0 = m(-3) - 2 Add 2 to both sides.
2 = m(-3) Divide by - 3
2/-3 = m
Now let's see what we have.
y = -2/3x - 2
C is the correct answer
