Answer:
The gradient = 1.4
The linear equation is y = 1.4x
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:
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute x₁ = 0, y₁ = 0, x₂ = 5, y₂ = 7 into the formula above
[tex]\begin{gathered} m\text{ = }\frac{7-0}{5-0} \\ m\text{ = }\frac{7}{5} \\ m\text{ = }1.4 \end{gathered}[/tex]
The point-slope form of the equation of a line is:
[tex]y-y_1=m(x-x_1)[/tex]
Substitute m = 1.4, x₁ = 0, y₁ = 0 into the equation above
[tex]\begin{gathered} y-0=1.4(x-0) \\ y=1.4x \end{gathered}[/tex]
The gradient = 1.4
The linear equation is y = 1.4x
