The two lines are parallel because their slopes are equal and their
y-intercepts are different
Step-by-step explanation:
Let us revise some rules
∵ The equation of line [tex]l_{1}[/tex] is y = 5x + 1
∵ The form of the equation is y = mx + c
∴ [tex]m_{1}[/tex] = 5
∴ [tex]c_{1}[/tex] = 1
∵ The equation of line [tex]l_{2}[/tex] is 2y - 10x + 3 = 0
- Put the equation in the form of y = mx + c
∵ 2y - 10x + 3 = 0
- Subtract 3 from both sides
∴ 2y - 10x = -3
- Add 10x to both sides
∴ 2y = 10x - 3
- Divide all terms by 2
∴ y = 5x - 1.5
∵ The form of the equation is y = mx + c
∴ [tex]m_{2}[/tex] = 5
∴ [tex]c_{2}[/tex] = -1.5
∵ [tex]m_{1}[/tex] = [tex]m_{2}[/tex]
∵ [tex]c_{1}[/tex] ≠ [tex]c_{2}[/tex]
∴ [tex]l_{1}[/tex] // [tex]l_{2}[/tex]
The two lines are parallel because their slopes are equal and their
y-intercepts are different
Learn more:
You can learn more about slopes of lines in brainly.com/question/12954015
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