The equation of the parallel line in slope-intercept form is;
y =
x - 
Step-by-step explanation:
Let us revise some facts about parallel lines
The equations of two parallel lines have:
- Same slopes
- Different y-intercept
The slope-intercept form of the equation of a line is y = m x + b, where m is the slope of the line and b is the y-intercept
The given line has equation 5x - 2y = 10
Put it in the form of y = m x + b to find its slope
∵ 5x - 2y = 10
- Subtract 5x from both sides
∴ -2y = 10 - 5x
- Divide to sides by -2
∴ y = -5 +
x
∴ y =
x - 5
- The value of m is the coefficient of x
∴ m = 
∴ The slope of the given line is 
∵ Parallel lines have same slopes
∴ The slope of the parallel line is m = 
- Substitute the value of m in the form of the equation
∴ The equation of the parallel line is y =
x + b
To find b substitute x and y in the equation by the coordinates of any point lies on the line
∵ The parallel line passes through point (3 , -5)
- Substitute x and y by the coordinates of the point (3 , -5)
∵ x = 3 and y = -5
∴ -5 =
(3) + b
∴ -5 =
+ b
- Subtract
from both sides
∴ b = 
∴ The equation of the parallel line is y =
x + 
∴ The equation of the parallel line is y =
x - 
The equation of the parallel line in slope-intercept form is;
y =
x - 
Learn more:
You can learn more about the equations of parallel lines in brainly.com/question/8628615
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