Question

What is the equation to the alope for this graph?

Answer 1

The equation of the line given is

y = (4x/3) - 8

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 just need to pick a point on the graph and calculate the slope of the line to write the equation of this 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}}=(y_2-y_1)/(x_2-x_1)`

For this question,

(x₁, y₁) and (x₂, y₂) are (6, 0) and (3, -4)

`\text{Slope = }(-4-0)/(3-6)=(-4)/(-3)=(4)/(3)`

So, picking the point (x₁, y₁) to be (6, 0)

Recall

y - y₁ = m (x - x₁)

m = slope = (4/3)

Point = (x₁, y₁) = (6, 0)

x₁ = 6

y₁ = 0

y - y₁ = m (x - x₁)

y - 0 = (4/3) (x - 6)

y = (4x/3) - 8

Hope this Helps!!!