equation of line parallel to 2x+3y=5
Answers
Answer:
2x+3y+k=o is parallel eq to 2x+3y=5
sub substitute the point in eq you can find value of k
Step-by-step explanation:
first, convert this equation into the slope-intercept form.
2x + 3y - 5 = 0
Add 5 to b oth sides, then subtract 2x from both sides, and then divide both sides by 3. Doing this will totally isolate y on one side of the equation:
2x + 3y - 5 = 0
2x + 3y = -5
3y = -2x - 5
y = -2/3*x - 5/3
Now we know the slope of the equation is -2/3. We are also given a point on a parallel line.
The product of the slopes of two parallel lines is always -1. Therefore, the slope of the line that passes through (2,-1) is 3/2 because -2/3 * 3–2 = -1.
So we have one equation and know its slope and y-interecept, and we know a point of another equation and also its slope.
Therefore, substitute for x and y - and include the slope - to write the equation for the line that passes through (2, -1):
y = mx + b
-1 = (3/2)(2) + b
How do we find B? First, perform the multiplication:
-1 = (6/2) + b
Reduce the fraction:
-1 = 3 + b
Subtract 3 from both sides:
b = -4
So the equation of the line that passes through (2,-1) is
y = (3/2)x - 4