In Exercises 39–48, give the slope and y-intercept of each line whose equation is given. Then graph the linear function. y = -2x/5+6

Verified step by step guidance

1. Identify the equation of the line in the slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
2. Compare the given equation \( y = -\frac{2}{5}x + 6 \) with the slope-intercept form to determine the slope \( m \) and the y-intercept \( b \).
3. From the equation, recognize that the slope \( m \) is \(-\frac{2}{5}\) and the y-intercept \( b \) is 6.
4. To graph the linear function, start by plotting the y-intercept (0, 6) on the coordinate plane.
5. Use the slope \(-\frac{2}{5}\) to find another point on the line. From the y-intercept, move down 2 units and right 5 units to plot the second point, then draw the line through these points.

Key Concepts

Slope

The slope of a line measures its steepness and direction, represented as 'm' in the slope-intercept form of a linear equation, y = mx + b. In this equation, 'm' indicates how much y changes for a unit change in x. A positive slope means the line rises as it moves from left to right, while a negative slope indicates it falls.

Y-Intercept

The y-intercept is the point where the line crosses the y-axis, represented as 'b' in the slope-intercept form y = mx + b. This value indicates the output (y) when the input (x) is zero. In the given equation, the y-intercept is 6, meaning the line intersects the y-axis at the point (0, 6).

Graphing Linear Functions

Graphing a linear function involves plotting points that satisfy the equation and connecting them to form a straight line. The slope indicates the angle of the line, while the y-intercept provides a starting point on the graph. By using the slope to find additional points from the y-intercept, one can accurately represent the linear relationship visually.