Question

What is a equation of the line that passes through the point (−5,7) and is parallel to the line x+5y=10

Answer 1

Answer:

7=-1/5x+6 is the answer

Answer 2

Answer:

$\displaystyle y = -\frac{1}{5} x +6$

Step-by-step explanation:

Equation of a LIne

The point-slope form of the equation of a line is:

y - k = m ( x - h )

Where m is the slope and (h,k) is a point through which the line passes.

We are required to find the equation of a line that passes through the point (-5,7) and is parallel to the line x+5y=10.

This information provides us the values of h=-5 and k=7. We now need to determine the value of the slope.

Two parallel lines have equal values for the slopes. The equation of the line

x + 5y = 10

Can be rearranged in such a way we can find its slope. Let's solve it for y:

5y = -x + 10

$y = -\frac{1}{5}+2$

The slope of this line is -1/5 and that is the same value of the slope of our line, thus its equation is:

$\displaystyle y - 7 = -\frac{1}{5} ( x + 5 )$

Adding 7:

$\displaystyle y = -\frac{1}{5} ( x + 5 )+7$

Operating:

$\displaystyle y = -\frac{1}{5} x + -\frac{1}{5}*5 +7$

$\displaystyle y = -\frac{1}{5} x -1+7$

$\boxed{\displaystyle y = -\frac{1}{5} x +6}$