Question

Write down the equations for the lines whose graphs are depicted below.

Answer 1

The graph depicts a linear equation

The equation of the graph is: $\mathbf{y = 2x }$

From the graph, we have the following points:

$\mathbf{(x_1,y_1) = (0,0)}$

$\mathbf{(x_2,y_2) = (2,1)}$

So, the slope (m) is:

$\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}$

This gives

$\mathbf{m = \frac{2-0}{1 -0}}$

$\mathbf{m = \frac{2}{1}}$

$\mathbf{m = 2}$

The equation is then calculated as:

$\mathbf{y = m(x - x_1) + y_1}$

This gives

$\mathbf{y = 2(x - 0) + 0}$

$\mathbf{y = 2(x - 0)}$

$\mathbf{y = 2x }$

Hence, the equation of the graph is: $\mathbf{y = 2x }$

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