Question Video: Finding the Intersection Point of Two Straight Lines

Find the intersection of the lines 𝑥 + 13 = 7 and 𝑦 − 16 = 0.

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Video Transcript

Find the intersection of the lines 𝑥 plus 13 equals seven and 𝑦 minus 16 equals zero.

We can find the intersection of two straight lines using an algebraic or graphical method. In this question, we notice that both of our equations only have one variable or unknown. This means that we can solve the equation 𝑥 plus 13 equals seven to calculate a value of 𝑥. Subtracting 13 from both sides of the equation gives us 𝑥 is equal to seven minus 13. The right-hand side is equal to negative six. Therefore, 𝑥 is equal to negative six. In the same way, we can solve the equation 𝑦 minus 16 equals zero by adding 16 to both sides. This gives us 𝑦 is equal to 16. The solutions of the two equations are 𝑥 equals negative six and 𝑦 equal 16. Therefore, the point of intersection of the two lines has coordinates negative six, 16.

This can also be shown on the 𝑥𝑦-coordinate plane. Any equation in the form 𝑥 equals 𝑎 where 𝑎 is some constant will correspond to a vertical line. This means that the equation 𝑥 is equal to negative six is a vertical line passing through negative six on the 𝑥-axis. Likewise, any equation in the form 𝑦 equals 𝑎 where 𝑎 is some constant will correspond to a horizontal line. The equation 𝑦 is equal to 16 is a horizontal line passing through the 𝑦-axis at 16. We can see from the figure that the two straight lines intersect at the point with coordinates negative six, 16. We can, therefore, conclude this is the point of intersection of the lines 𝑥 plus 13 equals seven and 𝑦 minus 16 equals zero.

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