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

Verified step by step guidance

1. Identify the given information: a point on the line \((2, -4)\) and the slope \(m = \frac{3}{4}\).
2. Use the point-slope form of the equation of a line: \(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\) is the given point.
3. Substitute the point \((2, -4)\) and the slope \(\frac{3}{4}\) into the point-slope form: \(y - (-4) = \frac{3}{4}(x - 2)\).
4. Simplify the equation to get it into slope-intercept form \(y = mx + b\) by distributing and isolating \(y\) on one side.
5. Use the simplified equation to plot the line by starting at the point \((2, -4)\) and using the slope \(\frac{3}{4}\) to find additional points.

Key Concepts

Slope of a Line

The slope represents the rate of change or steepness of a line, calculated as the ratio of the vertical change to the horizontal change between two points. In this problem, the slope m = 3/4 means the line rises 3 units for every 4 units it moves horizontally.

Point-Slope Form of a Line

The point-slope form is an equation of a line given a point (x₁, y₁) and slope m, expressed as y - y₁ = m(x - x₁). It is useful for writing the equation of a line when a point and slope are known, as in this problem with point (2, -4) and slope 3/4.

Graphing a Line

Graphing a line involves plotting a point and using the slope to find additional points. Starting at (2, -4), move up 3 units and right 4 units repeatedly to plot points, then draw a straight line through them to represent the line with slope 3/4.