Answer: y = - x/5 + 6
Step-by-step explanation:
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m is the slope
c is the y intercept
The given equation is
x + 5y = 10
5y = 10 - x
5y = - x + 10
Dividing both sides by 5, we have
5y/5 = - x/5 + 10/5
y = - x/5 + 2
By comparing this equation with the slope intercept equation,
m = - 1/5
If two lines are parallel, it means that the slope of both lines are equal. This means that the slope of the line passing through the point (- 5, 7)is - 1/5. We would find the equation of the line by substituting m = - 1/5, x = - 5 and y = 7 into the slope intercept equation. We have
7 = - 1/5 * - 5 + c
7 = 1 + c
c = 7 - 1
c = 6
By substituting m = - 1/5 and c = 6 into the slope intercept equation, the equation of the line that passes through the point (−5,7) and is parallel to the line x+5y=10 is
y = - x/5 + 6