What is the equation of the line, in slope-intercept form, that passes through (3, -1) and (-1, 5)?

Solution:

The equation of the line in slope-intercept form is given by y = mx + c ------(1)

Where, m = slope

c = y-intercept

The slope of the line can be found by using the formula m = (y₂ - y₁) / (x₂ - x₁)

Substituting the points (3, -1) and (-1,5) we get,

m = (5 + 1) / (-1 -3)

m = 6 / (-4)

m = -3/2

Next, find y-intercept using one of the points.

Let's take the point (-1,5)

5 = -3/2 (-1) + c

5 = 3/2 + c

c = 7/2

Put the value of c and m in (1)

y = -3/2(x) + 7/2

y = 1/2 [-3x + 7]

Therefore, the equation of line in slope-intercept form is y = 1/2 [-3x + 7].

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What is the equation of the line, in slope-intercept form, that passes through (3, -1) and (-1, 5)?

Summary:

The equation of the line, in slope-intercept form, that passes through (3, -1) and (-1, 5) is y = 1/2 [-3x + 7].