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zipit - 3. Find the equation of a line passing through (5, -6) parallel to:c) x + 3y=8 (e) x=7 (b) 3x + 5y = 7 (d) 7x - 12y = 5 (f) 2y = 5

Sagot :

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]