Answer:
[tex]\displaystyle y = -\frac{1}{5} x +6[/tex]
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
[tex]y = -\frac{1}{5}+2[/tex]
The slope of this line is -1/5 and that is the same value of the slope of our line, thus its equation is:
[tex]\displaystyle y - 7 = -\frac{1}{5} ( x + 5 )[/tex]
Adding 7:
[tex]\displaystyle y = -\frac{1}{5} ( x + 5 )+7[/tex]
Operating:
[tex]\displaystyle y = -\frac{1}{5} x + -\frac{1}{5}*5 +7[/tex]
[tex]\displaystyle y = -\frac{1}{5} x -1+7[/tex]
[tex]\boxed{\displaystyle y = -\frac{1}{5} x +6}[/tex]
