Question

Write the equation of a line passing through (2, 1) that is parallel to the line passing through (-1,2) and (0, -1)

Answer 1

y = -3x + 7 is the equation of a line passing through (2, 1) that is parallel to the line passing through (-1,2) and (0, -1)

Solution:

Given that, we have to write the equation of a line passing through (2, 1) that is parallel to the line passing through (-1,2) and (0, -1)

Find the slope of line

The slope of line is given by formula:

`m = (y_2-y_1)/(x_2-x_1)`

Here given that line is parallel to the line passing through (-1, 2) and (0, -1)

Therefore,

`(x_1, y_1) = (-1, 2)\\\\(x_2, y_2) = (0, -1)`

Substituting the values we get,

`m = (-1-2)/(0-(-1))\\\\m = (-3)/(1)\\\\m = -3`

Thus slope of line is -3

We know that, slopes of parallel lines are equal

Therefore, slope of line parallel to the line passing through (-1,2) and (0, -1) is also -3

Now find the equation of line with slope -3 and passing through (2, 1)

The equation of line in slope intercept form is given as:

y = mx + c ------ eqn 1

Where, "m" is the slope of line and "c" is the y intercept

Substitute m = -3 and (x, y) = (2, 1) in eqn 1

1 = -3(2) + c

1 = -6 + c

c = 7

Substitute m = -3 and c = 7 in eqn 1

y = -3x + 7

Thus the equation of line is found