Graph the line passing through the given point and having the indicated slope. Plot two points on the line. through (-2, 8), m = 2/5

Verified step by step guidance

1. Identify the given point and slope. The point is \((-2, 8)\) and the slope is \(m = \frac{2}{5}\).
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. Substitute \(x_1 = -2\), \(y_1 = 8\), and \(m = \frac{2}{5}\) to get: \(y - 8 = \frac{2}{5}(x + 2)\).
3. Simplify the equation to slope-intercept form \(y = mx + b\) by distributing and isolating \(y\): \(y = \frac{2}{5}x + \frac{2}{5} \times 2 + 8\).
4. Calculate the constant term (without final numeric evaluation) to express the full equation of the line in slope-intercept form.
5. To plot two points on the line, start with the given point \((-2, 8)\), then use the slope \(\frac{2}{5}\) to find another point by moving 5 units horizontally and 2 units vertically from the first point. Plot these two points and draw the line through them.

Key Concepts

Slope of a Line

The slope represents the rate of change of the line, defined as the ratio of the vertical change (rise) to the horizontal change (run) between two points. A slope of 2/5 means the line rises 2 units for every 5 units it moves horizontally.

Point-Slope Form of a Line

This form, y - y₁ = m(x - x₁), uses a known point (x₁, y₁) and the slope m to write the equation of a line. It helps in finding other points on the line by substituting values for x or y.

Plotting Points on a Coordinate Plane

Plotting involves marking points using their (x, y) coordinates on the Cartesian plane. To graph a line, start with the given point, then use the slope to find and plot a second point, ensuring accurate representation of the line.