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Find the equation of the line through (10, 4) that is parallel to the line with the equation

y = -1x + 3. Give the equation in standard form.

User Meriops
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1 Answer

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Answer:

x + y = 14

Explanation:

The question asks for the final answer to be an equation in standard form. The standard form of the equation for a line is ...

ax +by = c

where a, b, c are integers with no common factors, and 'a' is positive.

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When working with parallel and perpendicular lines, standard form is an easy form to work with. The coefficients (a and b) of parallel lines will be the same. All that is different between parallel lines is the value of 'c'.

Given this fact, it is convenient to start by putting the given equation into standard form. For that, we want the x-term on the same side of the equal sign as the y-term.

Adding x to both sides of the given equation puts it in standard form:

x +y = x +(-x) +3

x + y = 3 . . . . . simplified

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Now that we know our equation will be of the form ...

x + y = (some constant)

we need to find the constant. We can do that by using the given point values for x and y.

For the given point (x, y) = (10, 4), the constant for the parallel line will be ...

x + y = 10 + 4 = 14

x + y = 14 . . . equation of parallel line through (10, 4)

User Fernando Tiberti
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