graph and write the equation of the line

Question

parellel to the line 2x=7y+1 and passing through the point (1,-1)

Answer 1

First, remember that slope-intercept form of a line is:

 

y = mx + b,

 

where m = slope and b = y-intercept.

 

 

Two parallel lines have the same slope, so let's rearrange 2x = 7y + 1 into slope-intercept form to find its slope:

 

2x = 7y + 1

2x - 1 = 7y

(2/7)x - 1/7 = y

y = (2/7)x - 1/7

 

This means that the slope of your line is 2/7.

 

 

Finally, remember that point-slope form of a line is:

 

y - y₁ = m(x - x₁),

 

where m = slope and (x₁, y₁) = a point on the line.

 

 

You know that m = 2/7, and you're told that (x₁, y₁) = (1, -1) is a point on your line. Plug those into point-slope form to get:

 

y + 1 = 2/7(x - 1)

 

 

 

To graph your line, just plot (1, -1) and go up 2, right 7 to find a second point (since the slope, or rise/run, is 2/7). Connect those points.