Question

Complete the point-slope equation of the line through (-1,6) and (1,5). Use exact numbers.I NEED AN ANSWER PLEASE!!!

Answer 1

The equation of the line in point-slope form is

y - 6 = -0.5 (x + 1)

We can now simplify further

y - 6 = -0.5x - 0.5

y = -0.5x - 0.5 + 6

y = -0.5x + 5.5

This is the slope-intercept form

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 can use any one of the two points as the point in the equation.

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 (-1, 6) and (1, 5)

`\text{Slope = }(5-6)/(1-(-1))=(-1)/(1+1)=(-1)/(2)=-0.5`

Recall

y - y₁ = m (x - x₁)

m = slope = -0.5

Point = (x₁, y₁) = (-1. 6)

x₁ = -1

y₁ = 6

y - y₁ = m (x - x₁)

y - 6 = -0.5 (x - (-1))

y - 6 = -0.5 (x + 1)

We can now simplify further

y - 6 = -0.5x - 0.5

y = -0.5x - 0.5 + 6

y = -0.5x + 5.5

Hope this Helps!!!