Find the slope and \( y \)-intercept of the line. Graph the line. \( \frac{1}{7} y=x+1 \)

To find the slope and \( y \)-intercept, you'll want to rewrite the equation in slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept. Start with the original equation: \[ \frac{1}{7} y = x + 1 \] Multiply both sides by \( 7 \) to isolate \( y \): \[ y = 7x + 7 \] From this format, we can see that the slope \( m \) is \( 7 \) and the \( y \)-intercept \( b \) is \( 7 \). This means the line crosses the \( y \)-axis at the point \( (0, 7) \). To graph the line, start at the \( y \)-intercept \( (0, 7) \). From there, use the slope: rise \( 7 \) units and run \( 1 \) unit to the right to find another point \( (1, 14) \). Draw a straight line through these points, extending it in both directions for a complete graph. Now you have a lovely line that highlights its slope and intercept! 🎉