Question

Find the equation of the line that passes through (3,1) and is parallel to y=1−2x. Leave your answer in the form y=mx+c.

a) y=−2x+7
b) y=−2x−7
c) y=2x+7
d) y=2x−7

Answer 1

The equation of the line that passes through the point (3,1) and is parallel to the line given by y=1-2x is y = -2x + 7.

Step-by-step explanation:

To find the equation of the line that passes through the point (3,1) and is parallel to the line given by the equation y=1−2x, we must recognize that parallel lines have the same slope. Therefore, the slope of the new line will be the same as the slope of the given line, which is -2 (the coefficient of x in the equation).

We can use the point-slope form of a line's equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line (in our case, (3,1)) and m is the slope of the line. With our values, the equation becomes y - 1 = -2(x - 3). Simplifying this, we get y - 1 = -2x + 6, and then y = -2x + 7 after adding 1 to both sides.

Therefore, the equation of the line we are looking for is y = -2x + 7.