Question

Write the equation of the line with a constant rate of change of 1/2 through the point (6, -1).

a) y = 1/2x - 4
b) y = 1/2x + 4
c) y = 2x - 1
d) y = -2x + 13

Answer 1

The equation of the line with a slope of 1/2 through the point (6, -1) is y = 1/2x - 4, which matches option (a).

Step-by-step explanation:

The question asks us to write the equation of a line with a constant rate of change of ½ that passes through the point (6, -1). The rate of change in a linear equation is the same as the slope. Therefore, we are looking for a line with a slope of ½. The slope-intercept form of a linear equation is y = mx + b, where 'm' is the slope and 'b' is the y-intercept.

To find the correct equation, we need to use the given point to determine 'b'. We plug the coordinates into the slope-intercept equation:

y = ½x + b

-1 = ½(6) + b

b = -1 - ½(6) = -1 - 3 = -4

Therefore, the equation of the line is y = ½x - 4, which corresponds to option (a).