4 Amath tutor charge 75 for a 2 hour tutoring session and 225 for a 7 hour tutoring session. Write a linear equation to represent the charge y to hire the tutor for x hours. y=

To find the linear equation representing the charge \( y \) for \( x \) hours of tutoring, we need to determine the slope and the y-intercept of the equation.<br /><br />Given:<br />- $75 for 2 hours<br />- $225 for 7 hours<br /><br />First, let's find the slope \( m \):<br /><br />\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]<br /><br />Using the points (2, 75) and (7, 225):<br /><br />\[ m = \frac{225 - 75}{7 - 2} = \frac{150}{5} = 30 \]<br /><br />Now, we use the slope-intercept form \( y = mx + b \). We need to find the y-intercept \( b \).<br /><br />Using the point (2, 75):<br /><br />\[ 75 = 30(2) + b \]<br />\[ 75 = 60 + b \]<br />\[ b = 75 - 60 \]<br />\[ b = 15 \]<br /><br />So, the linear equation is:<br /><br />\[ y = 30x + 15 \]<br /><br />Therefore, the equation representing the charge \( y \) for \( x \) hours of tutoring is:<br /><br />\[ y = 30x + 15 \]