Given:
Point = (4, -9)
Slope = [tex]-\frac{5}{4}[/tex]
To find:
The equation of a line passes through the given point and slope.
Solution:
[tex]$m=-\frac{5}{4}[/tex]
[tex]x_1=4, y_1=-9[/tex]
Point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]$y-(-9)=-\frac{5}{4} (x-4)[/tex]
[tex]$y+9=-\frac{5}{4} (x-4)[/tex]
Multiply by 4 on both sides, we get
[tex]$4(y+9)=4\times -\frac{5}{4} (x-4)[/tex]
[tex]$4(y+9)=-5(x-4)[/tex]
[tex]$4y+36=-5x+20[/tex]
Subtract 36 from both sides.
[tex]$4y+36-36=-5x+20-36[/tex]
[tex]$4y=-5x-16[/tex]
Add 5x on both sides.
[tex]$5x+4y=5x-5x-16[/tex]
[tex]$5x+4y=-16[/tex]
The equation of a line is [tex]$5x+4y=-16[/tex].
