Question

A line that passes through points (2, 40) and (20, 4)

Answer 1

y - 40 = -2 (x - 2)

We can simplify this

y - 40 = -2x + 4

y = -2x + 4 + 40

y = -2x + 44

Step-by-step 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

We need to calculate the slope and to use one of the points given as (x₁, y₁)

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}}=(y_2-y_1)/(x_2-x_1)`

(x₁, y₁) and (x₂, y₂) are (2, 40) and (20, 4)

`\text{Slope = }(4-40)/(20-2)=(-36)/(18)=-2`

Slope = m = -2

(x₁, y₁) = (2, 40)

x₁ = 2, y₁ = 40

y - y₁ = m (x - x₁)

y - 40 = -2 (x - 2)

We can simplify this

y - 40 = -2x + 4

y = -2x + 4 + 40

y = -2x + 44

Hope this Helps!!!