The graph of the linear function passes through the points (4,24) and (6,30) What is the equation of the function? y=square x+?

To find the equation of the linear function, we need to determine the slope and the y-intercept.<br /><br />Step 1: Find the slope (m) using the given points $(4,24)$ and $(6,30)$.<br />The formula for finding the slope between two points is:<br />\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]<br /><br />Substituting the values from the given points:<br />\[ m = \frac{30 - 24}{6 - 4} = \frac{6}{2} = 3 \]<br /><br />So, the slope (m) is 3.<br /><br />Step 2: Use the slope-intercept form of a linear equation, which is:<br />\[ y = mx + b \]<br />where m is the slope and b is the y-intercept.<br /><br />We already have the slope (m = 3), so we can substitute one of the given points into the equation to solve for the y-intercept (b).<br /><br />Using the point $(4,24)$:<br />\[ 24 = 3(4) + b \]<br />\[ 24 = 12 + b \]<br />\[ b = 24 - 12 \]<br />\[ b = 12 \]<br /><br />So, the y-intercept (b) is 12.<br /><br />Step 3: Write the equation of the linear function using the slope (m) and y-intercept (b) we found.<br />\[ y = 3x + 12 \]<br /><br />Therefore, the equation of the linear function is:<br />\[ y = 3x + 12 \]