Equations of lines.

 

A line is given by \[ \ 2x - 3y + 4 = 0 \ \] Find the equation of the line parallel to the given line and passing through \( B(0, -2) \).

The gradient of the given line is needed as the gradient of the answer. Transform the expression for the line to gradient-intercept form.

\[ \begin {align} 3y &= 2x+ 4 \\ y &= 2/3x + 4/3 \end{align} \ \]

The point B is the y-intercept of the new line.

So the gradient-intercept form of the line is \[ \ y = 2/3x - 2 \ \]

Transform to the general form of the line. This means making the coefficient of x positive.

\[ \begin {align} 3y &= 2x - 6 \\ 2x - 3y - 6 &= 0 \end{align} \ \]

Important This is not a 'textbook on a screen' - this is an interactive learning system. Which means you have to 'act' to make it go.

Look through the options below and select the one you think is the best response. You will gain most benefit if you work the problem with pen and paper as you go, i.e. decide what you think is the correct option and write down what you think the result will be before you click. If the next step doesn't display, click another option.

 

What property of the given line must be used in the answer?

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Now You Try:

 

The x-intercept.
The gradient.
The y-intercept.