Video: Graphing a Linear Function Using Intercepts

Consider the linear equation 𝑦 = 2π‘₯ + 3. By finding the π‘₯- and 𝑦- intercepts, state the coordinates (0, 𝑦-intercept) and (π‘₯-intercept, 0) where the graph of the function crosses the axes. Hence, identify which of these is the line of the equation.

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Video Transcript

Consider the linear equation 𝑦 equals two π‘₯ plus three. By finding the π‘₯ and 𝑦 intercepts, state the coordinates zero, 𝑦-intercept and π‘₯-intercept, zero where the graph of the function crosses the axes.

In order to calculate the 𝑦-intercept, we need to substitute π‘₯ equals zero into the equation 𝑦 equals two π‘₯ plus three. This gives us 𝑦 is equal to two multiplied by zero plus three. Two multiplied by zero is zero. Adding three gives us an answer of 𝑦 equals three. Therefore, the point at which the line intercepts the 𝑦-axis is zero, three.

In the same way, we can work out the π‘₯-intercept by substituting 𝑦 equals zero into the equation 𝑦 equals two π‘₯ plus three. This gives us zero is equal to two π‘₯ plus three. Subtracting three from both sides of this equation gives us two π‘₯ is equal to negative three. And finally, dividing both sides of this equation by two give us a value of π‘₯ of negative three over two, negative three-halves.

This gives us the two coordinates where the graph of the function crosses the axes. It crosses the 𝑦-axis at zero, three. And it crosses the π‘₯-axis at negative three over two, zero.

The second part of the question asked us, hence, identify which of these is the line of the equation. Is it line A, line B, line C, line D, or line E.

As the line intercepts the 𝑦-axis at zero, three, this immediately rules out line A and line E. We also worked out that the graph intercepts the π‘₯-axis at negative three over two, negative one and a half, zero. Both line A and line D intercept the π‘₯-axis here. As we’ve already ruled out line A, the only line that passes through the points zero, three and negative three over two, zero is line D. This means that line D has equation 𝑦 equals two π‘₯ plus three.

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