SOLUTION: I need to find the standard form of he equation of the line that passes through the point (1,4) and is parallel to the line 7x+y=-3.

Algebra ->  Equations -> SOLUTION: I need to find the standard form of he equation of the line that passes through the point (1,4) and is parallel to the line 7x+y=-3.      Log On


   

Question 129083: I need to find the standard form of he equation of the line that passes through the point (1,4) and is parallel to the line 7x+y=-3.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Step 1: Solve the given equation for y, putting it into slope-intercept form (y=mx%2Bb).

7x%2By=-3
y=-7x-3

Step 2: By inspection of the coefficient on x of the slope-intercept form, determine the slope of the given line: m=-7.

Step 3: Two lines are parallel if and only if their slopes are equal, i.e. m%5B1%5D=m%5B2%5D. Therefore, the desired line must also have a slope of m=-7

Step 4: Use the point-slope form of the line (y-y%5B1%5D=m%28x-x%5B1%5D%29, the x- and y-coordinates of the given point, and the slope number from Step 3 to derive an equation for the desired line.

The given point is P(1,4), so x%5B1%5D=1 and y%5B1%5D=4.

y-4=-7%28x-1%29

Step 5: Put this new equation into standard form. Standard form is Ax%2BBy=C.

Distribute the -7 and remove parentheses:
y-4=-7x%2B7

Add 4 to both sides:
y=-7x%2B11

Add 7x to both sides:
7x%2By=11

Done.

The red line is the given line, and the green one is the derived one. At least they look like they are parallel.