Question

Find an equation of the line with the given slope that passes through the given point. Write the equation in the form Ax+By-C. m=-4; (-5, -1)

A.4x + y = -9
B.4x + y = -1
C.4x + y = -21
D.4x + y = 21.

Answer 1

Using the slope m=-4 and the point (-5, -1), the line equation is found using point-slope form, simplified, and rearranged to the standard form Ax+By=C, which results in 4x + y = -21, corresponding to option C.

Step-by-step explanation:

The student is asking to find the equation of a line with a given slope and that passes through a specific point. To write the equation in the standard form Ax+By=C, we will use the point-slope form y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point. Given m=-4 and the point (-5, -1), we first write the equation in point-slope form:

y - (-1) = -4(x - (-5))

Simplify and distribute:

y + 1 = -4x - 20

Then we isolate y to get it into slope-intercept form:

y = -4x - 20 - 1

y = -4x - 21

Now to put it into the form Ax+By=C, we rearrange the equation:

4x + y = -21

This corresponds to option C. Therefore, the answer is 4x + y = -21.