Question

Write the equation of a line parallel to the line determined by the points( -2,1) and (0,5 ) passing through the point (1,4)

Answer 1

y = 2x + 2

Explanation:

Find the slope of the line that passes through the points (-2, 1) and (0, 5):

`\implies \textsf{slope}\:(m)=(y_2-y_1)/(x_2-x_1)=(5-1)/(0-(-2))=(4)/(2)=2`

If two lines are parallel they have the same slope.

Therefore, the slope of the other line that passes through point (1, 4) is also 2.

To find the equation of the parallel line that passes through the point (1, 4), substitute the found slope of 2 and the point (1, 4) into the point-slope formula:

`\implies y-y_1=m(x-x_1)`

`\implies y-4=2(x-1)`

`\implies y-4=2x-2`

`\implies y=2x+2`