Question

1) Find the equation of the line through the points (-2, 5) and (3, 1). Also, graph this line.

Answer 1

Answer

The equation of the line is

y - 5 = -0.8 (x + 2)

We can then simplify further

y - 5 = -0.8x - 1.6

y = -0.8x - 1.6 + 5

y = -0.8x + 3.4

Explanation

The general form of the equation in point-slope form is

y - y₁ = m (x - x₁)

where

y = y-coordinate of a point on the line.

y₁ = This refers to the y-coordinate of a given point on the line

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

x₁ = x-coordinate of the given point on the line

So, for this, we just need to solve for the slope and use one of the two points given to find the equation of the line.

For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as

$Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}$

For this question,

(x₁, y₁) and (x₂, y₂) are (-2, 5) and (3, 1)

x₁ = -2

y₁ = 5

x₂ = 3

y₂ = 1

$\text{Slope = }\frac{1-5}{3-(-2)}=\frac{-4}{3+2}=\frac{-4}{5}=-0.8$

Recall

y - y₁ = m (x - x₁)

m = slope = -0.8x

(x₁, y₁) = point = (-2, 5)

x₁ = -2

y₁ = 5

y - y₁ = m (x - x₁)

y - 5 = -0.8 (x - (-2))

y - 5 = -0.8 (x + 2)

We can then simplify further

y - 5 = -0.8x - 1.6

y = -0.8x - 1.6 + 5

y = -0.8x + 3.4

Hope this Helps!!!