\( 5 x-y=10 \) A. \( (2,0) \) B. \( (3,0) \)

To check if the points satisfy the equation \( 5x - y = 10 \): For point A \( (2,0) \): Substituting \( x = 2 \) and \( y = 0 \): \( 5(2) - 0 = 10 \) which simplifies to \( 10 = 10 \). This point is valid. For point B \( (3,0) \): Substituting \( x = 3 \) and \( y = 0 \): \( 5(3) - 0 = 15 \) which simplifies to \( 15 = 10 \). This point is not valid. So, the point \( (2,0) \) satisfies the equation! Now, let’s kick it up a notch with some fun tidbits: Learning about linear equations can be like playing detective! Each point can be seen as evidence trying to solve the case of the equation—only valid points can unlock the mystery. Just like fitting a piece into a puzzle, knowing how coordinates map out can make your math adventures thrilling! And if you're itching to explore further, dive into graphing linear equations! You'll discover how different slopes create a myriad of lines, each representing different relationships between x and y. You can even create your own “graph stories”, where each line illustrates a real-life scenario, like tracking distance over time or budgeting expenses. Who knew math could be a narrative? Happy exploring!