Find the equation of the line parallel to the line 3x + y = 5 and containing the point (4, – 2).
y=-3x+5
When lines are parallel with one another, they must have the same slope. Otherwise one line would cross the other because of the difference in steepness. They also can't be overlapping one another, so they have to cross the y axis at a different place.
Therefore, the -3x would have to be the slope of the parallel line and the y-intercept could NOT also be 5, otherwise the two lines would be overlapping.
So we have:
y=-3x+b
Plug in x and y from the given point:
-2=-3(4)+b
Solve for b, replace the 4 and -2 back to x and y, and you have the equation of the line parallel to the line 3x+y=5 and containing the point (4, -2).
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To find the equation of a line parallel to the line 3x + y = 5, we need to determine the slope of the given line. The equation of a line can be represented in the form y = mx + b, where m represents the slope of the line.
To find the slope of the line 3x + y = 5, we need to rearrange the equation in the form y = mx + b.
Given: 3x + y = 5
Rearranging the equation:
y = 5 - 3x
Now, we can observe that the coefficient of x is -3, which is the slope of the line.
A line parallel to this line will have the same slope. So, the slope of the line we are looking for is also -3.
Now, we have an advanced form of the equation: y = -3x + b.
To find the value of b, we can substitute the coordinates of the given point (4, -2) into the equation:
-2 = -3(4) + b
Simplifying:
-2 = -12 + b
b = -2 + 12
b = 10
We now have the slope, -3, and the y-intercept, 10. So, the equation of the line parallel to the line 3x + y = 5 and containing the point (4, -2) is:
y = -3x + 10.