Question

What is the equation, in point-slope form, for a line that goes through (8, −4)(8, −4) and has a slope of −56−56 ?

a. y−4=−56(x+8)
b. y+4=−56(x+8)
c. y+4=−56(x−8)
d. y−4=−56(x−8)

Answer 1

The correct equation in point-slope form for a line through the point (8, −4) with a slope of −56 is y + 4 = −56(x − 8), which is option (c)

Step-by-step explanation:

The question asks to find the equation of a line in point-slope form that passes through the point (8, −4) with a slope of −56. Point-slope form is expressed as y − y1 = m(x − x1), where (x1, y1) is a point on the line and m is the slope.

Given the point (8, −4) and the slope −56, we substitute into the formula to obtain the equation y + 4 = −56(x − 8). This corresponds to the correct option (c).

Note the signs: y has a negative value at the given point, thus y + 4 becomes zero when y = −4; similarly, x minus 8 equals zero when x = 8, which agrees with the given point.