Question

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?

Answer 1

To find the equation of a line parallel to 2x + y = 6 that passes through (4, -4), first find the slope of the original line (which is -2). Then, using the point-slope form with the point (4, -4) and the slope -2, the equation of the new line is y = -2x + 4.

Step-by-step explanation:

Finding the Equation of a Parallel Line

To find the equation of a line that is parallel to another line and passes through a given point, first, we need to determine the slope of the original line. The equation 2x + y = 6 can be rearranged to the slope-intercept form y = mx + b, where m represents the slope. Subtracting 2x from both sides gives us y = -2x + 6, indicating the slope, m, is -2. Since parallel lines have equal slopes, the new line will also have a slope of -2.

Now, we use the point-slope form y - y1 = m(x - x1) to write the equation for our new line, which passes through point (4, -4). Plugging in the point and the slope, we get y - (-4) = -2(x - 4). Simplifying this equation gives us y + 4 = -2x + 8, and further simplifying yields the final equation: y = -2x + 4.