Write an equation of the line parallel to the line given by 3x-2y=8 and having the same y- intercept as the line given by 2y+3x=-4
3x - 2y = 8.
3x + 2y = -4.
Parallel lines have equal slopes:
m = -A/B = -3/-2 = 3/2 = Slope.
Let x = 0:
3*0 + 2y = -4,
y = -2 = y-int.
Eq: y = (3/2)x - 2.
To find the equation of a line that is parallel to a given line, we need to consider two things: the slope of the given line and the y-intercept of the desired line.
First, let's find the slope of the given line. Rewrite the equation 3x - 2y = 8 in slope-intercept form, which is y = mx + b, where m represents the slope:
3x - 2y = 8
-2y = -3x + 8
y = (3/2)x - 4
From this equation, we can see that the slope of the given line is 3/2.
Since the desired line is parallel to the given line, it will have the same slope of 3/2.
Now, let's consider the y-intercept of the desired line. The equation of the given line with the y-intercept is 2y + 3x = -4. We need to find the value of y when x = 0, as this will give us the y-intercept.
Substitute x = 0 into the equation: 2y + 3(0) = -4
2y = -4
y = -2
So the y-intercept of the given line is -2.
Now we have the slope (m = 3/2) and the y-intercept (b = -2) for the desired line. We can write the equation of the desired line as:
y = (3/2)x - 2