Answer:
y +5 = 3 / 4 ( x + 4)
Explanation:
The equation of a line in slope-intercept form is given by
[tex]y=mx+b[/tex]where
m = slope
b = y-intercept.
Now we are told that the slope of our line is m = 3/4; therefore, our equation is
[tex]y=\frac{3}{4}x+b[/tex]Now, what is the value of b?
To find out, we use the fact that the line passes through (-4, -5); therefore, it must satsify x = -4, y = -5. Putting x = -4 and y = -5 into the above equation gives
[tex]-5=\frac{3}{4}(-4)+b[/tex]Simplifying the above gives
[tex]-5=-\frac{12}{4}+b[/tex][tex]\Rightarrow-5=-3+b[/tex]Finally, adding 3 to both sides of the equation gives
[tex]-5+3=b[/tex][tex]b=-2[/tex]With the value of b in hand, we can now write the equation of the line:
[tex]\boxed{y=\frac{3}{4}x-2}[/tex]The above equation is our final answer!
