What is an equation of the line that passes through the point left bracket, 4, comma, minus, 4, right bracket(4,−4) and is parallel to the line 2, x, plus, y, equals, 62x+y=6
To find an equation of the line that is parallel to the line 2x+y=6, we need to determine the slope of the given line.
The line 2x+y=6 can be written in slope-intercept form as y=-2x+6. Now we can see that the slope of this line is -2.
Since the line we are looking for is parallel to the given line, it will also have a slope of -2.
Using the point-slope form of a linear equation, we can write the equation of the line that passes through the point (4,-4) and has a slope of -2:
y - y1 = m(x - x1)
Substituting the values of (x1,y1) = (4,-4) and m = -2 into the equation:
y - (-4) = -2(x - 4)
Simplifying:
y + 4 = -2x + 8
y = -2x + 4
Therefore, an equation of the line that passes through the point (4,-4) and is parallel to the line 2x+y=6 is y = -2x + 4.