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Debora [2.8K]
3 years ago
15

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

Mathematics
1 answer:
Feliz [49]3 years ago
8 0

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)

<em><u>Solution:</u></em>

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

<em><u>The slope of line is given by formula:</u></em>

m = \frac{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 = \frac{-1-2}{0-(-1)}\\\\m = \frac{-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)

<em><u>The equation of line in slope intercept form is given as:</u></em>

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

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

<em><u>Substitute m = -3 and (x, y) = (2, 1) in eqn 1</u></em>

1 = -3(2) + c

1 = -6 + c

c = 7

<em><u>Substitute m = -3 and c = 7 in eqn 1</u></em>

y = -3x + 7

Thus the equation of line is found

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