Write an equation for line L in point-slope form and slope-intercept form.

Verified step by step guidance

1. Identify the slope of the given line y = 3x + 2. Since the equation is in slope-intercept form y = mx + b, the slope m is 3.
2. Since line L is parallel to y = 3x + 2, it has the same slope. So, the slope of line L is also 3.
3. Use the point-slope form of a line equation, which is \(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\) is a point on the line and m is the slope. Here, the point is (-1, 2) and the slope is 3.
4. Substitute the point (-1, 2) and slope 3 into the point-slope form: \(y - 2 = 3(x - (-1))\) or \(y - 2 = 3(x + 1)\).
5. To write the equation in slope-intercept form, simplify the point-slope form by distributing the slope and solving for y: \(y - 2 = 3x + 3\), then add 2 to both sides to get \(y = 3x + 5\).

Key Concepts

Slope of Parallel Lines

Parallel lines have the same slope. Since line L is parallel to y = 3x + 2, it shares the slope of 3. This means the rate of change for line L is identical to the given line, which is essential for writing its equation.

Point-Slope Form of a Line

The point-slope form is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line. This form is useful when you know a point on the line and its slope, allowing you to write the equation directly from given information.

Slope-Intercept Form of a Line

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. After finding the slope and using a point to solve for b, this form provides a clear way to express the line's equation and easily graph it.