In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (-2, 0) and (0, 2)

Verified step by step guidance

1. Identify the two points given: \((-2, 0)\) and \((0, 2)\).
2. Calculate the slope \(m\) using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Substitute the points into the formula: \(m = \frac{2 - 0}{0 - (-2)}\).
3. Use the point-slope form of the equation, which is \(y - y_1 = m(x - x_1)\). Choose one of the points, for example, \((-2, 0)\), and substitute \(m\) and the point into the equation.
4. Simplify the point-slope form equation to get the slope-intercept form \(y = mx + b\).
5. Substitute the slope \(m\) and one of the points into the slope-intercept form to solve for \(b\), the y-intercept.

Key Concepts

Point-Slope Form

Point-slope form of a linear equation is expressed as y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. This form is particularly useful for writing equations when you know a point on the line and the slope, allowing for quick derivation of the line's equation.

Slope-Intercept Form

Slope-intercept form is given by the equation y = mx + b, where m represents the slope and b is the y-intercept. This format is beneficial for easily identifying the slope and where the line crosses the y-axis, making it straightforward to graph the line.

Calculating Slope

The slope of a line measures its steepness and is calculated as the change in y divided by the change in x (m = (y2 - y1) / (x2 - x1)). For the points (-2, 0) and (0, 2), the slope can be determined, which is essential for both point-slope and slope-intercept forms of the equation.