If \( y=a x+b \) with \( y=5 \) when \( x=2 \)

To find the values of \( a \) and \( b \), we can plug in the values from the equation \( y = ax + b \). Substituting \( y = 5 \) and \( x = 2 \) gives you the equation \( 5 = 2a + b \). This is just one equation with two unknowns, which means we need another condition to find unique values for \( a \) and \( b \). So, to nail down specific values, we either need a second point or some additional information about the relationship. One common approach for problems like this is to assign a value, like setting \( a = 1 \) for simplicity, and then solving it from there. If we say \( a = 1 \), we would solve \( 5 = 2(1) + b \) to find \( b = 3 \). Thus, we have a specific solution of \( y = 1x + 3 \). This method of testing values can help avoid the complications of algebra when you're in need of a quick solution!