The line 2y+3x=24 and y=mx+1 are parallel. Find the value of m
y=−34x+2.75
the two lines must have the same slope
The line 2y+3x=24 has slope -3/2
so, ...
To determine if two lines are parallel, we can look at their slopes. Two lines are parallel if and only if their slopes are equal.
First, let's find the slope of the line 2y+3x=24. We rewrite the equation in slope-intercept form (y = mx + b) by isolating y:
2y + 3x = 24
2y = -3x + 24
y = (-3/2)x + 12
Comparing this equation to y = mx + b, we can see that the slope (m) is -3/2.
Now, we can compare the slope of the line 2y + 3x = 24 to the slope of y = mx + 1. Since the two lines are parallel, their slopes must be equal:
-3/2 = m
Therefore, the value of m is -3/2.