Question

Find the equation of the line through point (10,4) and parallel to 3x+5y=8.

Answer 1

Parallel = same slope
Find slope of 3x + 5y = 8
Turn into y = mx + b
5y = -3x + 8
Divide by 5
y = -3/5x + 8/5
Slope is -3/5
Y = -3/5x + b, find y intercept
Plug in the point
4 = -3/5(10) + b
4 = -6 + b, b = 10
Final equation: y = -3/5x + 10

Answer 2

$3x+5y=50$ is the equation of the line through point (10,4) and parallel to 3x+5y=8.

How to solve equation of the line through point and parallel to a given line?

We can write the equation of a line parallel to a given line if we know a point on the line and an equation of the given line. y=2x+3 . Parallel lines have the same slope. The slope of the line with equation y=2x+3 is 2 .

Given

Equation of the line is 3x + 5y = 8.

Point = (10, 4)

First we find the slope of the line  3x + 5y = 8 by replacing it into slope intercept form:

$3x + 5y = 8$

⇒ $5y = -3x + 8$

⇒ $y = \frac{-3}{5} x + \frac{8}{5}$

Therefore, the slope of the line is m = $\frac{-3}{5}$.

Now since the equation of the line with slope m passing through a point $(y-y_{1} )=m(x-x_{1})$

⇒ $y - 4=\frac{-3}{5} (x-10)$

⇒ $5(y-4)=-3(x-10)$

⇒ $5y-20=-3x+30$

⇒ $3x+5y=30+20$

⇒ $3x+5y=50$

Hence, $3x+5y=50$ is the equation of the line through point (10,4) and parallel to 3x+5y=8.

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