Question

Line passes through (-1, 5) and (3,-1)

Answer 1

Answer:

Answer: The Equation of the Line Passing through the given Points (-1, 5), (1, 3) is x + y = 4.

Step-by-step explanation:

Given: (x1, y1) = (-1, 5) and (x2, y2) = (1, 3)

Let's calculate the slope below,

According to the Slope Formula,

(m) = (y2 − y1) / (x2 − x1)

Substituting the values,

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

m = -2/2

m = -1

The point-slope formula states (y − y1) = m (x − x1).

Substituting the values of (x1, y1) = (-1, 5) and m = -1, we get,

(y - 5) = -1 × (x - (-1))

⇒ y - 5 = - x - 1

⇒ x + y = 4

Hence, the equation of the line passing through the given points (-1, 5), (1, 3) is x + y = 4.

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Answer 2

Answer:

$\frac{ - 1 - 5}{3 + 1} = \frac{y - 5}{x + 1} \\ \frac{ - 6}{4} = \frac{y - 5}{x + 1} \\ \frac{ - 3}{2} = \frac{y - 5}{x + 1} \\ - 3(x + 1) = 2(y - 5) \\ - 3x - 3 = 2y - 10 \\ 2y = - 3x - 7 \\ \boxed{y = - \frac{3}{2} x + \frac{7}{2} } \\ alternative:\ method\\ y = mx + c \\ 5 = - m + c...(1) \\ - 1 = 3m + c...(2) \\ (2) - (1) \\ - 6 = 4m \rightarrow \: m = - \frac{6}{4} = - \frac{3}{2} \\sub \: in...(1) \\ 5 = - ( - \frac{3}{2} ) + c \\ c = 5 - \frac{3}{2} \\ c = \frac{7}{2} \\\boxed{y = - \frac{3}{2} x + \frac{7}{2}}$