Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b (3,6); x+5y= 8
anyone knows the answer to this question?
easiest way:
since the new equation is parallel to the given line x + 5y = 8
the new line will differ only in the constant.
New line: x + 5y = c
plug in the given point (3,6) ...
3 + 30 = c = 33
new line: x + 5y = 33
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What they want .....
given line: x + 5y = 8
5y = -x + 8
y = (-1/5)x + 8/5
so the slope of the line must be -1/5
new line: y = (-1/5)x + b , they must have the same slope
plug in the point (3,6)
6 = (-1/5)(3) + b
6 = -3/5 + b
b = 6 + 3/5 = 33/5
new equation : y = (-1/5)x + 33/5
which is the same as my equation done the easy way
To find the equation of a line that is parallel to the given line, we need to determine the slope of the given line.
First, let's rearrange the equation:
x + 5y = 8
Subtracting x from both sides:
5y = -x + 8
Dividing both sides by 5:
y = (-1/5)x + 8/5
The slope of the given line is -1/5.
Since a line parallel to the given line has the same slope, the new line will have a slope of -1/5 as well.
Now we have the slope (-1/5) and a point (3,6) that the line passes through. We can use the point-slope form of a line to find the equation:
y - y1 = m(x - x1)
Substituting the given values:
y - 6 = (-1/5)(x - 3)
Distributing the slope:
y - 6 = (-1/5)x + 3/5
Rearranging the equation to the standard form, y = mx + b:
y = (-1/5)x + 3/5 + 6
Combining the constants:
y = (-1/5)x + 3/5 + 30/5
Simplifying the fractions:
y = (-1/5)x + 33/5
Therefore, the equation of the line parallel to x + 5y = 8 and passing through the point (3,6) is: y = (-1/5)x + 33/5.