(2) Two lines intersect at the point \( (1,3) \). The \( y \)-intercepts of the lines are 1 and 2 What are the equations of the lines?

To find the equations of the two lines, we can use the point-slope form of a line equation. The point \( (1,3) \) is on both lines, and we know the \( y \)-intercepts are \( 1 \) and \( 2 \). For the first line with a \( y \)-intercept of \( 1 \): - The equation can be written as \( y = mx + 1 \). - To find the slope \( m \), substitute the point \( (1,3) \): \( 3 = m(1) + 1 \) → \( m = 2 \). - Thus, the first line's equation is \( y = 2x - 1 \). For the second line with a \( y \)-intercept of \( 2 \): - The equation is \( y = mx + 2 \). - Again, substitute the point \( (1,3) \): \( 3 = m(1) + 2 \) → \( m = 1 \). - Thus, the second line's equation is \( y = x + 2 \). The equations of the two lines are: 1. \( y = 2x - 1 \) 2. \( y = x + 2 \)