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 (show work) I am stuck with this problem. Can you please show me how to do these types of equations? Thank you
3x-2y = 8
-2y = -3x+8
y = 3/2 -4 slope = 3/2
2y + 3x = -4
2y = -3x -4
y =-3/2 -2 y-intercept = -2
Now use y = mx + b to write your equation
To find the equation of a line that is parallel to the line 3x - 2y = 8, we need to determine the slope of the given line first.
We can rewrite the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Start by isolating y:
3x - 2y = 8
-2y = -3x + 8
y = (3/2)x - 4
From this equation, we can see that the slope of the line is 3/2.
Now, to find the equation of a line parallel to this line, we know that the slope will be the same, which means the slope of our new line is also 3/2.
Next, we are given that the new line should have the same y-intercept as the line given by 2y + 3x = -4. To determine the y-intercept of the given line, we can rearrange the equation:
2y + 3x = -4
2y = -3x - 4
y = (-3/2)x - 2
Therefore, 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 new line.
Plugging these values into the slope-intercept form equation, y = mx + b, we get:
y = (3/2)x - 2
So, the equation of the line parallel to the line 3x - 2y = 8 and having the same y-intercept as the line 2y + 3x = -4 is y = (3/2)x - 2.