Question

(2,-1);5x-7y=8 write an equation of a line containing the given point and parallel to the given line

Answer 1

• 5x-7y=8

Isolate y

• 7y=5x-8
• y=5/7x-8/7

Here

• m=5/7

Parallel lines have equal slope

Point(2,-1)

Equation of line in point slope form

`\\ \sf\longmapsto y-y_1=m(x-x_1)`

`\\ \sf\longmapsto y+1=5/7(x-2)`

`\\ \sf\longmapsto 7y+7=5x-10`

`\\ \sf\longmapsto 5x-7y-17=0`

Answer 2

• 5x - 7y = 17

Explanation:

Given line:

• 5x - 7y = 8

Convert the equation into slope-intercept form:

• 5x - 7y = 8
• 7y = 5x - 8
• y = 5/7x - 8/7

The line parallel to this has same slope of 5/7 and passes through the point (2, - 1).

Use point-slope form and convert the equation into standard form:

• y - (- 1) = 5/7(x - 2)
• y + 1 = 5/7x - 10/7
• 7y + 7 = 5x - 10
• 5x - 7y = 7 + 10
• 5x - 7y = 17