Question

Which is an equation in point-slope form for the line that passes through the points (−1,4) and (3,−4)? Responses y−3=−2(x+4) y minus 3 equals negative 2 open parenthesis x plus 4 close parenthesis y+4=2(x−3) y plus 4 equals 2 open parenthesis x minus 3 close parenthesis y−4=2(x+3) y minus 4 equals 2 open parenthesis x plus 3 close parenthesis y+4=−2(x−3)

Answer 1

m = (-4 - 4)/(3 - (-1)) = -8/4 = -2

y + 4 = -2(x - 3)

Answer 2

To find the equation in point-slope form for the line passing through the points (−1,4) and (3,−4), we calculate the slope (−2) and then use one point to write the equation y - 4 = −2(x + 1).

Step-by-step explanation:

To find the equation of the line in point-slope form that passes through the given points (−1,4) and (3,−4), we first need to calculate the slope of the line (m). The slope is derived from the change in y over the change in x (rise over run).

The formula to find the slope (m) is:

m = (y2 - y1) / (x2 - x1)

Using the given points (−1,4) and (3,−4), we can substitute in as follows:

m = (−4 - 4) / (3 - (−1))

m = (−8) / (4)

m = −2

With the slope calculated, the point-slope form of the line can be written as:

y - y1 = m(x - x1)

Using one of the given points, for instance (−1,4), the equation becomes:

y - 4 = −2(x - (−1))

Which simplifies to:

y - 4 = −2(x + 1)

Therefore, the equation in point-slope form for the line that passes through the points (−1,4) and (3,−4) is y - 4 = −2(x + 1).