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.

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) (Show Source): You can put this solution on YOUR website!
Step 1: Solve the given equation for y, putting it into slope-intercept form ().

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

Step 3: Two lines are parallel if and only if their slopes are equal, i.e. . Therefore, the desired line must also have a slope of

Step 4: Use the point-slope form of the line (, 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 and .

Step 5: Put this new equation into standard form. Standard form is .

Distribute the -7 and remove parentheses:

Add 4 to both sides:

Add 7x to both sides:

Done.

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

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