Question

Write the equation of the line, in slope-intercept form, that has a slope of 3/4 and contains the point (-1,-8).

A. y = (3/4)x - 8
B. y = (-4/3)x - 8
C. y = (4/3)x - 8
D. y = (-3/4)x - 8

Answer 1

To find the equation of the line with slope 3/4 through the point (-1, -8), plug the slope and point coordinates into the slope-intercept equation and solve for the y-intercept. The correct equation is y = (3/4)x - 29/4, which is not among the provided options.

Step-by-step explanation:

The question asks to write the equation of the line in slope-intercept form that has a slope (m) of 3/4 and passes through the point (-1, -8). The slope-intercept form of a line is given by y = mx + b, where m represents the slope and b represents the y-intercept of the line. Since we are given a slope of 3/4 and a point on the line (-1, -8), we can substitute these values into the slope-intercept formula and solve for b, the y-intercept.

Substituting into the formula:

y = (3/4)x + b
-8 = (3/4)(-1) + b
-8 = -3/4 + b
-8 + 3/4 = b
b = -32/4 + 3/4
b = -29/4

So, the complete equation of the line is:

y = (3/4)x - 29/4

Therefore, none of the given options A, B, C, or D are correct.