Question

The equation of the line that goes through the point (1,5) and is parallel to the line 3x+5y=2 can be written in the form y=Mx+b

Answer 1

Answer:

$y=-\frac{3}{5}x+\frac{28}{5}$

Step-by-step explanation:

step 1

Find the slope of the given line

we have

$3x+5y=2$

isolate the variable y

$5y=-3x+2\\\\y=-\frac{3}{5}x+\frac{2}{5}$

The slope of the given line is

$m=-\frac{3}{5}$

step 2

Find the equation of the line that goes through the point (1,5) and is parallel to the given line

Remember that

If two lines are parallel then their slopes are equal

therefore

we have

$m=-\frac{3}{5}$

$point\ (1,5)$

substitute in the equation of a line in slope intercept form

$y=mx+b$

$5=-\frac{3}{5}(1)+b$

solve for b

$b=5+\frac{3}{5}\\\\b=\frac{28}{5}$

substitute

$y=-\frac{3}{5}x+\frac{28}{5}$