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Write the equation of the line, in standard form, that passes through the origin and is parallel to x + y= 6. Include your work in you
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Write the equation of the line, in standard form, that passes through the origin and is parallel to x + y= 6. Include your
work in your final answer. Type your answer in the box provided or use the upload option to submit your solution
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Mathematics
4 years
2021-08-28T07:20:33+00:00
2021-08-28T07:20:33+00:00 1 Answers
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Answer:
x+y=0
Step-by-step explanation:
Hi there!
We’re given the line x+y=6 and we want to write the equation of the line that’s parallel to x+y=6 and passes through the origin (or the point (0,0)) in standard form
Standard form is given as ax+by=c, where a, b, and c are free integer coefficients (the values of a, b, and c are numbers).
Note that a CANNOT be 0 and CANNOT be negative
First, let’s find the slope of the line that will be parallel to x+y=6, as parallel lines have the same slope.
We’ll do this by converting x+y=6 from standard form into slope-intercept form (y=mx+b, where m is the slope and b is the y intercept)
x+y=6
subtract x from both sides
y=-x+6
although there’s no number in front of x, there’s the negative sign, which means that the slope of x+y=6 is -1
Since parallel lines have the same slope, the slope of the new, parallel line is also -1
here’s our equation so far in slope-intercept form:
y=-x+b
we need to find b
As the line will pass through (0,0), we can substitute it into the equation to solve for b
substitute 0 as x and 0 as y into the equation
0=-(0)+b
multiply
0=0+b
0=b
so the equation in slope-intercept form is y=-x+0
But remember! The problem asks for the answer in standard form
in that case, add x to both sides of the equation
x+y=0
Hope this helps!