Find the equation of the line parallel to 4x=5y=7 and passing through (3,2) leave answer in y=mx+b
Since the = and the + signs are on the same key , I will assume you meant:
4x + 5y = 7 as the given line.
Since the new line must be parallel to the given one, it will differ only in the constant
new line: 4x + 5y = c
but (3,2) lies on it, so
12 + 10 = c = 22
4x + 5y = 22
or
y = (-4/5)x + 22/5
To find the equation of a line that is parallel to the given line and passes through the point (3,2), we can use the following steps:
1. Rewrite the equation of the given line: 4x - 5y = 7. Let's rearrange this equation to make it easier to work with. Subtract 4x from both sides: -5y = -4x + 7.
2. Divide both sides of the equation by -5 to solve for y: y = (4/5)x - 7/5. Now we have the equation of the given line in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
3. Since we want to find a line that is parallel to this line, the new line will also have a slope of (4/5). So, the equation of the new line will be: y = (4/5)x + b.
4. To determine the value of b, substitute the coordinates of the point (3,2) into the equation and solve for b. We have: 2 = (4/5)(3) + b. Multiply (4/5) by 3: 2 = 12/5 + b. To get rid of the fraction, multiply both sides by 5: 10 = 12 + 5b. Subtract 12 from both sides: -2 = 5b. Divide both sides by 5: b = -2/5.
5. Now we have the slope (m = 4/5) and the y-intercept (b = -2/5). Plug these values into the equation: y = (4/5)x - 2/5.
Therefore, the equation of the line parallel to 4x - 5y = 7 and passing through (3,2) is: y = (4/5)x - 2/5.