Question

What is the equation of the line in slope-intercept form that has a slope of -3 and passes through (15,-2)?

A. y = -3x + 4
B. y = -3x - 4
C. y = -x + 4
D. y = -x - 4

Answer 1

The

equation

of the line with a slope of -3 that passes through (15, -2) is y = -3x + 43, which is not among the options provided. Thus, there appears to be an error in the options.

Step-by-step explanation:

The student is asking for the equation of a line in

slope-intercept

form, which is given by

y = mx + b

, where

m

is the slope and

b

is the y-intercept. Given a slope of -3 and that the line passes through the point (15, -2), we can use the point-slope form to find the y-intercept,

b

.

Starting with the slope-intercept form:

y = mx + b

We plug in the slope (m = -3) and the coordinates of the point (15, -2):

y = -3x + b

-2 = -3(15) + b

Solving for

b

, we get:

b = 45 - 2

which simplifies to

b = 43

.

Therefore, the equation of the line is:

y = -3x + 43

However, none of the options provided match

y = -3x + 43

. Therefore, it seems there is an error in the given options.

Answer 2

The correct equation of the line with a slope of -3 passing through the point (15, -2) is y = -3x + 43. The provided options do not include the correct equation. However, none of the options given (A, B, C, D) match the correct equation, which is y = -3x + 43.

Step-by-step explanation:

The question asks about the equation of the line in slope-intercept form with a given slope and point it passes through. The slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. To find the equation of the line with slope -3 that passes through the point (15, -2), we use the point-slope formula:

y - y1 = m(x - x1), substituting the point (15, -2) and slope -3 into this formula to get:

y - (-2) = -3(x - 15)

y + 2 = -3x + 45

Finally, by isolating y on one side, we get:

y = -3x + 45 - 2

y = -3x + 43

However, none of the options given (A, B, C, D) match the correct equation, which is y = -3x + 43.