Question

On a coordinate plane, a line goes through (negative 3, 3) and (negative 2, 1). A point is at (4, 1). What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (4, 1)? y − 1 = −2(x − 4) y – 1 = Negative one-half(x – 4) y – 1 = One-half(x – 4) y − 1 = 2(x − 4)

Answer 1

The equation of the line parallel to the given line and passing through (4, 1) is (y - 1) = -2(x - 4). This is obtained by using the same slope of the original line, which is -2.

Step-by-step explanation:

To find the equation of a line parallel to the given line and passing through the point (4, 1), we must first calculate the slope of the given line. The slope (m) is the rise over the run between two points on the line. Using the points (-3, 3) and (-2, 1), the slope is given by (1-3)/(-2+3) = -2/1 = -2. Since parallel lines have the same slope, the line through (4, 1) will also have a slope of -2.

The point-slope form of the equation of a line with slope m and passing through a point (x1, y1) is given by (y - y1) = m(x - x1). Plugging in the slope and the coordinates of the given point (4, 1) into this formula, we get (y - 1) = -2(x - 4). This is the equation of the line parallel to the given line that passes through (4, 1).

Answer 2

y - 1 = -2(x - 4).

Step-by-step explanation:

First, we need to find the slope. Two sets of coordinates are (-3, 3), and (-2, 1).

(3 - 1) / (-3 - -2) = 2 / (-3 + 2) = 2 / (-1) = -2.

The line will be parallel to the given line, so the slope is the same.

Now that we have a point and the slope, we can construct an equation in point-slope form.

y1 = 1, x1 = 4, and m = -2.

y - 1 = -2(x - 4).

Hope this helps!