Answer for question #1: y= [tex]\frac{2x}{3}[/tex]+ 6
Step-by-step explanation:
1. Find the equation of the line parallel to the line y=2x/3−2 passing through the point (−3,4).
The equation of the line in the slope-intercept form is y=2x/3−2.
The slope of the parallel line is the same: m=23.
So, the equation of the parallel line is y=2x/3+a.
To find a, we use the fact that the line should pass through the given point: 4=(23)⋅(−3)+a.
Thus, a=6.
Therefore, the equation of the line is y=2x/3+6.
Answer: y=2x/3+6.
