Questions: find a) Write equation of lines b) The slope dx and y-intercept d) determine where increasing or decreasing

Solution Steps

For line L1, we can identify two points: (-1, 0) and (0, 1). For line L2, we can identify two points: (0, 2) and (2, 0).

The slope \( m \) of a line passing through points \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

For L1: \[ m_1 = \frac{1 - 0}{0 - (-1)} = \frac{1}{1} = 1 \]

For L2: \[ m_2 = \frac{0 - 2}{2 - 0} = \frac{-2}{2} = -1 \]

The equation of a line in slope-intercept form is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

For L1: Using the point (0, 1): \[ y = 1x + 1 \] So, the equation is: \[ y = x + 1 \]

For L2: Using the point (0, 2): \[ y = -1x + 2 \] So, the equation is: \[ y = -x + 2 \]

Final Answer