Question

Write an equation of the line, point-slope form, that passes through the two given points. Points: (-3,3), (9,-3)

Answer 1

y - 3 = -0.5 (x + 3)

To silmplify, we multiply through by 2

2y - 6 = -1 (x + 3)

2y - 6 = -x - 3

2y = -x - 3 + 6

2y = -x + 3

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

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

To calculate the slope,

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)`

For this question,

(x₁, y₁) and (x₂, y₂) are (-3, 3) and (9, -3)

x₁ = -3

y₁ = 3

x₂ = 9

y₂ = -3

`\text{Slope = }(-3-3)/(9-(-3))=(-6)/(9+3)=(-6)/(12)=-(1)/(2)=-0.5`

Using the first point given as (x₁, y₁)

(x₁, y₁) = (-3, 3)

x₁ = -3, y₁ = 3

Recall that

y - y₁ = m (x - x₁)

m = -0.5

y - 3 = -0.5 (x - (-3))

y - 3 = -0.5 (x + 3)

To silmplify, we multiply through by 2

2y - 6 = -1 (x + 3)

2y - 6 = -x - 3

2y = -x - 3 + 6

2y = -x + 3

Hope this Helps!!!