Question

Choose the equation that represents a line that passes through points (−1, 2) and (3, 1).

Answer 1

the equation of this line is y = (-1/4)x + 7/4

Explanation:

As we go from (−1, 2) to (3, 1), x increases by 4 and y decreases by 1. Thus, the slope of the line connecting these points is m = rise / run = -1/4.

Find the equation of this line in slope-intercept form, y = mx + b. Substitute 1 for y and 3 for x and calculate b:

1 = (-1/4)(3) + b, or

4/4 = -3/4 + b, or

7/4 = b.

Then the equation of this line is y = (-1/4)x + 7/4.

Answer 2

You did not provide us with equations to select.

Find the slope m.

m = (1 - 2)/(3 - (-1))

m = -1/(3 + 1)

m = -1/4

Use the slope and one of the points and plug into the point-slope formula.

y - 1 = (-1/4)(x - 3)

Isolate y.

y - 1 = (-1/4)x + (3/4)

y = (-1/4)x + (3/4) + 1

y = (-1/4)x + (7/4)

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