Question

The equation of a line L1 is y=5x+1

The equation of L2 is 2y-10x+3=0
Show that these 2 lines are parallel

Answer 1

Parallel lines have equal slopes

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 this form with slope m = 5

rearrange 2y - 10x + 3 = 0 into this form

add 10x to both sides

2y + 3 = 0 + 10x ( subtract 3 from both sides )

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

y = 5x - ← in slope- intercept form with slope m = 5

Since both lines have a slope of 5 then they are parallel lines

Explanation:

hope this helps

Answer 2

Lines are considered parallel if their slopes are the same. In Line 1, the slope is 5 and in Line 2, when we solve for 'y', we also get a slope of 5, which means the two lines are parallel.

Explanation:

In order to find slope, it is easiest to put the equation in slope-intercept form, or y=mx + b, where m = slope and b=y-intercept. In L1, y=5x +1 indicates a slope of 5. In L2, the equation is not in slope-intercept form, so we must solve for 'y' using inverse operations: 2y - 10x +3 = 0, start by subtracting 3 from both sides of the equal sign: 2y - 10x +3 -3 = 0 - 3 gives us 2y - 10x = -3. Then add '10x' to both sides: 2y - 10x + 10x = -3 + 10x gives us 2y = 10x - 3. Lastly, divide all terms by 2: 2y/2 = (10/2)x - 3/2 or y = 5x - 1.5. Now that L2 is in slope-intercept form, we can see that m=5 as in L1, so since they have the same slope, they are parallel lines.