Does the point two, negative three lie on the line 𝑦 equals five 𝑥 minus seven?
Let’s think about the line with equation 𝑦 equals five 𝑥 minus seven. This line contains all of the ordered 𝑥, 𝑦 pairs such that the 𝑦-value is seven less than five times the 𝑥-value. To determine whether any point lies on this line, we need to consider whether its coordinates satisfy this equation. The 𝑦-coordinate of this point is the second value in the ordered pair, so it’s negative three. The 𝑥-coordinate is the first value in this ordered pair; it is two.
Substituting 𝑥 equals two into the expression on the right-hand side of the equation of this line gives five multiplied by two minus seven. That is 10 minus seven, which is equal to three. Now, three is not equal to negative three, which means that the 𝑥-value of two and the 𝑦-value of negative three do not satisfy the equation 𝑦 equals five 𝑥 minus seven.
This means that the point with coordinates two, negative three does not to lie on the line 𝑦 equals five 𝑥 minus seven. And so our answer to the question is no.