Question

Points Write the equation in point slope form using the pair of points (-6, 4) and (-1,0)

Answer 1

y - 4 = (-4/5) (x + 6)

We can then simplify further by multiplying through by 5

5y - 20 = -4 (x + 6)

5y - 20 + 20 = -4x - 24 + 20

5y = -4x - 4

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

Now, we need 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 (-6, 4) and (-1, 0)

x₁ = -6

y₁ = 4

x₂ = -1

y₂ = 0

`\text{Slope = }(0-4)/(-1-(-6))=(-4)/(-1+6)=(-4)/(5)`

Slope = m = (-4/5)

We can then use any of the points given as the point in the equation

(x₁, y₁) = (-6, 4)

x₁ = -6, y₁ = 4

y - y₁ = m (x - x₁)

y - 4 = (-4/5) (x - (-6))

y - 4 = (-4/5) (x + 6)

We can then simplify further by multiplying through by 5

5y - 20 = -4 (x + 6)

5y - 20 + 20 = -4x - 24 + 20

5y = -4x - 4

Hope this Helps!!!