Two lines intersect at a point 𝐴, as shown. Circle the coordinates of point 𝐴. Is it negative two, negative eight; negative eight, negative two; negative one-half, negative eight; or negative eight, eight?
We’re given the equation for two different lines and shown the place where they intersect, point 𝐴. Since we’re not given a full grid, it’s best not to try and solve this problem by graphing. Instead, we’ll take these two equations, 𝑦 equals 𝑥 cubed and 𝑦 equals negative eight, and set them equal to each other.
By plugging in negative eight for the 𝑦-value of our first function, our new equation says negative eight equals 𝑥 cubed. We’re asking the question for what value of 𝑥 will the 𝑦-value be equal to negative eight.
The 𝑥 is being cubed here. To get 𝑥 by itself, we’ll take the cube root of 𝑥 cubed. And if we take the cube root on the right side of the equation, we must take the cube root on the left side of the equation. The cube root of negative eight equals negative two. The cube root of 𝑥 cubed equals 𝑥.
And that means when 𝑥 equals negative two, 𝑦 equals negative eight. When 𝑥 is negative two, 𝑦 equals negative eight, which means point 𝐴’s location is negative two, negative eight.