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Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 5x + 1 ← is in slope- intercept form

with slope m = 5

L2 has equation 2y - 10x + 3 = 0

add 10x to both sides

2y + 3 = 10x ( subtract 3 from both sides )

2y = 10x - 3 ( divide all terms by 2 )

y = 5x - ← in slope- intercept form

with slope m = 5

Parallel lines have equal slopes , thus

L1 and L2 are parallel lines

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The equation y = 2x + c is in slope- intercept form

with slope m = 2

Calculate the slope between the given points and equate to 2

Calculate m using the slope formula

m =

with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (k, 10)

m = = = 2 ( multiply both sides by 2 )

2k = 13 ( divide both sides by 2 )

k = 6.5

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The equation of the line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = , thus

y = x + c ← is the partial equation

To find c substitute (4, - 2) into the partial equation

- 2 = 2 + c ⇒ c = - 2 - 2 = - 4

y = x - 4 ← equation of line

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step-by-step explanation: