Question

Complete the point-slope equation of the line through (1, 3) and (5, 1). Use exact numbers.​

Answer 1

Answer:

$The \ equation \ in \ point \ and \ slope \ form \ is; \ y - 3 = -\dfrac{1}{2} \cdot (x - 1)$

Step-by-step explanation:

The coordinates of the points through which the line passes are (1, 3) and (5, 1)

The slope, m, of a line given the coordinates of two known points on the line, (x₁, y₁), (x₂, y₂) can be found as follows;

$Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

The slope of the given line is therefore $m =\dfrac{1-3}{5-1} = \dfrac{-2}{4} = -\dfrac{1}{2}$

The equation of the line in point and slope form is therefore, y - y₁ = m·(x - x₁) or y - y₂ = m·(x - x₂)

Therefore, by substituting the known values, we have the equation in point and slope form as follows;

$y - 3 = -\dfrac{1}{2} \cdot (x - 1)$