5x + y = -28
Step-by-step explanation:
Hi there!
We're given that a line has a slope of -5 and contains the point (-4, -8)
We want to write the equation of this line in standard form
Standard form is given as ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be zero, and a cannot be negative
Before we write the equation in standard form however, we need to write it in slope-intercept form, which is y=mx+b, where m is the slope & b is the y intercept
As we are already given the slope, we can immediately plug that in for m in y=mx+b
y=-5x+b
Now to find b:
As the equation passes through the point (-4, -8), we can use its values to help solve for b
Substitute -4 as x and -8 as y:
-8 = -5(-4) + b
Multiply
-8 = 20 + b
Subtract 20 from both sides
-8 = 20 + b
-20 -20
__________
-28 = b
substitute -28 as b
y = -5x - 28
We found the equation in slope-intercept form, but remember, we want it in standard form
In standard form, both x and y are on the same side; so, let's move 5x to the other side; to do this, we need to add 5x to both sides
y = -5x - 28
+5x +5x
_________
5x + y = -28
Hope this helps!