Equation of a line passing through the point (5, -6) and parallel to 3x + 5y = 7
First find the slope of the equation 3x + 5y = 7
Re-arrange
5y = -3x + 7
Divide through by 5
[tex]y=-\frac{3}{5}\text{x + }\frac{7}{5}[/tex]compare the above with y = mx + b
slope (m) = -3/5
Parallel equations have same slope
The slope of the equatiion is -3/5
substitute
x₁ = 5 y₁=-6 m=-3/5 in the formula below
y- y₁ = m(x - x₁)
[tex]y+6=-\frac{3}{5}(x\text{ -5)}[/tex][tex]y\text{ + 6 =}\frac{-3}{5}x\text{ +3}[/tex][tex]\frac{3}{5}x\text{ + y = 3-6}[/tex][tex]\frac{3}{5}x+y=-3[/tex][tex]3x+\text{ 5y =-15}[/tex]