Question

Write an equation in point-slope form of the line that passes through the point (4, 7) and has a slope of -1.

a) y - 7 = -1(x - 4)
b) y = x - 3
c) y - 4 = -1(x - 7)
d) y = -x + 11

Answer 1

The equation of the line in point-slope form passing through (4, 7) with a slope of -1 is y - 7 = -1(x - 4), and the slope for a line passing through (1, 0.1) and (7, 26.8) is approximately 4.5.

Step-by-step explanation:

The equation in point-slope form of the line that passes through the point (4, 7) with a slope of -1 is given by:

y - y1 = m(x - x1),

where (x1, y1) is the point the line passes through and m is the slope.

Substituting the given point (4, 7) and the slope (-1), we get:

y - 7 = -1(x - 4).

Therefore, the correct answer is:

a) y - 7 = -1(x - 4)

To calculate the slope for a line passing through two points, you can use the following formula:

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

Applying this to the points given, (1, 0.1) and (7, 26.8):

m = (26.8 - 0.1) / (7 - 1) = 26.7 / 6 = 4.45,

which is approximately 4.5 when rounded to one decimal place. Hence, the correct option is:

b) 4.5