Answer:
[tex]y = -\frac{1}{4}x - 2[/tex]
Step-by-step explanation:
i'm not sure if you're trying to find the equation of the line ?? but i'll assume that's the case and find the slope-intercept form equation of the line.
slope intercept form is [tex]y = mx + b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept. since the slope is already identified, you can plug in [tex]-\frac{1}{4}[/tex] for [tex]m[/tex].
plug in the [tex]x[/tex] and [tex]y[/tex] values from the coordinate pair that passes through the line, which is (-4, -1). you can start with either [tex]x[/tex] or [tex]y[/tex], but i'm going to start with [tex]x[/tex].
first, plug in [tex]-4[/tex] for [tex]x[/tex].
now plug in [tex]-1[/tex] for [tex]y[/tex].
after plugging in all of the given values, the equation is now [tex]-1 = -\frac{1}{4}(-4)+b[/tex], in which you need to solve for [tex]b[/tex].
now it's time to solve! begin by multiplying [tex]-\frac{1}{4}(-4)[/tex] in order to simplify the right side of the equation.
you now have [tex]-1 = 1 + b[/tex]. subtract 1 from both sides of the equation. on the right side, it cancels itself out, leaving you with [tex]b[/tex]. on the left side of the equation, you now have [tex]-1 - 1[/tex], which equals [tex]-2[/tex].
therefore [tex]-2 = b[/tex], or [tex]b = -2[/tex].
now that you've solved for your [tex]b[/tex] value, plug it into your initial slope-intercept form equation!
if you want to check to make sure that the values are correct, plug (-4, -1) into your completed slope-intercept form equation. as you did in the beginning, plug in [tex]-4[/tex] for [tex]x[/tex] and [tex]-1[/tex] for [tex]y[/tex].
begin simplifying by multiplying [tex]-\frac{1}{4}(-4)[/tex].
subtract [tex]1 - 2[/tex].
since both sides of the equation are equal, that means your [tex]b[/tex] value of [tex]-2[/tex] is correct because it makes the equation true!
aaaand there you go! i hope this helps. have a great day! <3
