College Algebra

Question

Write an equation of the line passing through ​(−4​,5​) and having slope −6. Give the answer in​ slope-intercept form.

Answer 1

Hello, thank you for taking the time to post your question!

The slope-intercept form that we’re trying to get to here is y = mx + b, where “m” is the slope and “b” is the y-intercept.

On this question we’re given the slope directly, m = -6. From there then you want to plug in the point (-4, 5) into the equation in order to solve for the value of “b”

y = -6x + b

5 = -6(-4) + b

5 = 24 + b

-19 = b

Putting it all together then makes the equation here

y = -6x - 19

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

(y-5)/(x+4) = -6 = slope = difference in y coordinates divided by difference in x coordinates ("rise over run")

y-5 = -6x -24

y = -6x -19 in slope intercept form. -6 = slope, -19 = y intercept

or

y=mx +b

y=-6x + b, calculate b by plugging in x=-4, y = 5

5 =-6(-4) + b

b = 5-24 = -19

y= -6x -19