Question Video: Finding the Equation of a Line Passing through a Given Point and Parallel to a Given Line

What is the equation of the straight line that passes through the point (1, 2) and that is parallel to the line 𝑦 = βˆ’5?

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Video Transcript

What is the equation of the straight line that passes through the point one, two and that is parallel to the line 𝑦 equals negative five?

So let’s have a look at this point one, two which would be here on the grid. We need to find the line which passes through this point and which is parallel to the line 𝑦 equals negative five. When we have a line like 𝑦 equals negative five, what we’re really saying is that the 𝑦-value must always be negative five and the π‘₯-value can be anything. For example, on this line, we could have one, negative five; three, negative five; or even negative two, negative five. The line which passes through all of these points with a 𝑦-value of negative five is in fact the line 𝑦 equals negative five. When we’re given the equation of a line that just has a 𝑦-variable, then this will give us a horizontal line.

The line that we’re looking for that passes through the point one, two must also be a horizontal line. It’s going to have just one variable in the equation which is going to be 𝑦, and the 𝑦-intercept will give us the constant term. So 𝑦 is equal to two. We can check this by remembering that this will mean that every 𝑦-value on this line would be two. So we could have the coordinate three, two on this line or five, two on this line or even negative four, two. In all of these cases, the 𝑦-value in each ordered pair will be two. So the answer then that the equation of the straight line passing through the point one, two and parallel to 𝑦 equals negative five is the line 𝑦 equals two.

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