Answer:
see explanation
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
-------------------------------------------------------------
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
--------------------------------------------------------------
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