Question

Find the gradient and find the linear equation represented by the graph

Answer 1

Answer:

The gradient = 1.4

The linear equation is y = 1.4x

Step-by-step explanation:

Since the line passes through the origin, the two points that can be identified on the line are (0, 0) and (5, 7)

where x₁ = 0, y₁ = 0, x₂ = 5, y₂ = 7

Find the gradient using the formula:

`m\text{ = }(y_2-y_1)/(x_2-x_1)`

Substitute x₁ = 0, y₁ = 0, x₂ = 5, y₂ = 7 into the formula above

`\begin{gathered} m\text{ = }(7-0)/(5-0) \\ m\text{ = }(7)/(5) \\ m\text{ = }1.4 \end{gathered}`

The point-slope form of the equation of a line is:

`y-y_1=m(x-x_1)`

Substitute m = 1.4, x₁ = 0, y₁ = 0 into the equation above

`\begin{gathered} y-0=1.4(x-0) \\ y=1.4x \end{gathered}`

The gradient = 1.4

The linear equation is y = 1.4x