Question

Write the standard form of the equation of the line through the given points.

(-2, 2) and (-5, 5)

Answer 1

The standard form of the equation of the line is y = -x, which represents a line with a slope of -1 passing through the points (-2, 2) and (-5, 5).

Step-by-step explanation:

To find the standard form of the equation of the line through the given points (-2, 2) and (-5, 5), we can use the point-slope form of the equation of a line: y - y1 = m(x - x1), where (x1, y1) are the coordinates of one point on the line, and m is the slope of the line.

Step 1: Find the slope of the line using the formula m = (y2 - y1) / (x2 - x1)

= (5 - 2) / (-5 - (-2))

= 3 / -3

= -1.

Step 2: Use one of the given points, (-2, 2), and the slope -1 in the point-slope form y - y1 = m(x - x1):

1. y - 2 = -1(x - (-2))
2. y - 2 = -1(x + 2)
3. y - 2 = -x - 2
4. y = -x - 2 + 2
5. y = -x

Therefore, the standard form of the equation of the line is y = -x, which represents a line with a slope of -1 passing through the points (-2, 2) and (-5, 5).