Which line below is parallel to y=-2/3x+5?
a. 2x-3y=6
b. 2x+3y=6
c. 3x-2y=6
d. 3x+2y=6
To determine which line is parallel to y = -2/3x + 5, we need to compare the slopes of the given lines. The given equation is in slope-intercept form (y = mx + b), where the coefficient of x (m) represents the slope of the line.
The slope of the line y = -2/3x + 5 is -2/3, which means any line parallel to it must have the same slope.
Now let's determine the slopes of the lines in the options:
a. 2x - 3y = 6
To write this equation in slope-intercept form, we need to isolate y:
-3y = -2x + 6
y = (2/3)x - 2
The slope of this line is 2/3, which is NOT equal to -2/3. Therefore, option a is not parallel to the given line.
b. 2x + 3y = 6
To write this equation in slope-intercept form, we need to isolate y:
3y = -2x + 6
y = (-2/3)x + 2
The slope of this line is -2/3, which is equal to the slope of the given line. Therefore, option b is parallel to y = -2/3x + 5.
c. 3x - 2y = 6
To write this equation in slope-intercept form, we need to isolate y:
-2y = -3x + 6
y = (3/2)x - 3
The slope of this line is 3/2, which is NOT equal to -2/3. Therefore, option c is not parallel to the given line.
d. 3x + 2y = 6
To write this equation in slope-intercept form, we need to isolate y:
2y = -3x + 6
y = (-3/2)x + 3
The slope of this line is -3/2, which is NOT equal to -2/3. Therefore, option d is not parallel to the given line.
In conclusion, the line parallel to y = -2/3x + 5 is option b.