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+3=-4
first equation:
2y=3x-8
y=3/2 x -4
you have the slope, so theline parallel to this has a slope of 3/2
second equation:
2y=hmmmm. where is the x?
anyway,find the y intercept (where x is zero).
then, your equation is y=3/2 x +yntercept
thank you
To find the equation of a line parallel to the line given by 3x - 2y = 8, we need to determine the slope of the given line.
Step 1: Rewrite the given line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
3x - 2y = 8
-2y = -3x + 8
y = (3/2)x - 4
From the slope-intercept form, we can see that the slope (m) of the given line is 3/2.
Step 2: Since we are looking for a line parallel to the given line, the slope of the new line will also be 3/2.
Step 3: To determine the y-intercept of the new line, we need to find the y-intercept of the line given by 2y + 3 = -4.
Step 4: Rewrite the line in slope-intercept form.
2y + 3 = -4
2y = -4 - 3
2y = -7
y = -7/2
From the slope-intercept form, we can see that the y-intercept of the given line is -7/2.
Step 5: Use the slope-intercept form (y = mx + b) and the previously determined slope and y-intercept to write the equation of the new line.
y = (3/2)x - 7/2
Therefore, the equation of the line parallel to 3x - 2y = 8 and with the same y-intercept as 2y + 3 = -4 is y = (3/2)x - 7/2.