The equation of the parallel line in slope-intercept form is;
y = [tex]\frac{5}{2}[/tex] x - [tex]\frac{25}{2}[/tex]
Step-by-step explanation:
Let us revise some facts about parallel lines
The equations of two parallel lines have:
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 + [tex]\frac{5}{2}[/tex] x
∴ y = [tex]\frac{5}{2}[/tex] x - 5
- The value of m is the coefficient of x
∴ m = [tex]\frac{5}{2}[/tex]
∴ The slope of the given line is [tex]\frac{5}{2}[/tex]
∵ Parallel lines have same slopes
∴ The slope of the parallel line is m = [tex]\frac{5}{2}[/tex]
- Substitute the value of m in the form of the equation
∴ The equation of the parallel line is y = [tex]\frac{5}{2}[/tex] 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 = [tex]\frac{5}{2}[/tex] (3) + b
∴ -5 = [tex]\frac{15}{2}[/tex] + b
- Subtract [tex]\frac{15}{2}[/tex] from both sides
∴ b = [tex]\frac{-25}{2}[/tex]
∴ The equation of the parallel line is y = [tex]\frac{5}{2}[/tex] x + [tex]\frac{-25}{2}[/tex]
∴ The equation of the parallel line is y = [tex]\frac{5}{2}[/tex] x - [tex]\frac{25}{2}[/tex]
The equation of the parallel line in slope-intercept form is;
y = [tex]\frac{5}{2}[/tex] x - [tex]\frac{25}{2}[/tex]
Learn more:
You can learn more about the equations of parallel lines in brainly.com/question/8628615
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