Question

The equation of the line with slope -1 that goes through the point (-9,-4) can be written in the form y=mx+b

Answer 1

To find the equation of the line with a slope of -1 going through (-9, -4), we use the point-slope form, insert the given point, solve for the y-intercept, b, and write the equation as y = -x - 13.

Step-by-step explanation:

The student has asked for the equation of a line with a slope of -1 that passes through the point (-9, -4). The general equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

To find the equation of this specific line, we insert the slope m = -1 and the point (-9, -4) into the equation y = mx + b, and solve for b. Starting with the equation:

y = (-1)x + b

We substitute the x and y values from the point (-9, -4):

-4 = (-1)(-9) + b

Then simplify and solve for b:

-4 = 9 + b

b = -4 - 9

b = -13

Now we have both the slope and the y-intercept, so the equation of the line is:

y = -1x - 13

Or simply:

y = -x - 13