Graph the line satisfying the given conditions.through (2, -4), m = 3/4

Verified step by step guidance

1. Start by identifying the point-slope form of a line equation: \( y - y_1 = m(x - x_1) \), where \( m \) is the slope and \( (x_1, y_1) \) is a point on the line.
2. Substitute the given point \((2, -4)\) and the slope \(m = \frac{3}{4}\) into the point-slope form equation.
3. The equation becomes \( y + 4 = \frac{3}{4}(x - 2) \).
4. To graph the line, you can convert this equation to the slope-intercept form \( y = mx + b \) by solving for \( y \).
5. Once in slope-intercept form, identify the y-intercept and use the slope to plot the line starting from the point \((2, -4)\).

Key Concepts

Slope-Intercept Form

The slope-intercept form of a linear equation is expressed as y = mx + b, where m represents the slope and b is the y-intercept. This form is useful for quickly identifying the slope of the line and where it crosses the y-axis, allowing for easy graphing of linear equations.

Point-Slope Form

Point-slope form is another way to express a linear equation, given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. This form is particularly helpful when you know a point on the line and the slope, as it allows you to derive the equation of the line directly.

Graphing a Line

Graphing a line involves plotting points that satisfy the linear equation and connecting them to form a straight line. To graph a line given a point and a slope, you can start at the given point and use the slope to find additional points by moving vertically and horizontally according to the rise over run ratio.