In Exercises 39–48, give the slope and y-intercept of each line whose equation is given. Then graph the linear function. f(x) = -2x+1

Verified step by step guidance

1. Identify the given linear function: \(f(x) = -2x + 1\).
2. Recall that a linear function in slope-intercept form is written as \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
3. Compare the given function \(f(x) = -2x + 1\) to the slope-intercept form to find the slope \(m = -2\) and the y-intercept \(b = 1\).
4. To graph the function, start by plotting the y-intercept point at \((0, 1)\) on the coordinate plane.
5. From the y-intercept, use the slope \(-2\) (which means a rise of \(-2\) and a run of \$1$) to find another point by moving down 2 units and right 1 unit, then draw the line through these points.

Key Concepts

Slope of a Linear Function

The slope represents the rate of change of the function and indicates how steep the line is. It is the coefficient of x in the equation f(x) = mx + b, where m is the slope. A negative slope means the line decreases as x increases.

Y-Intercept of a Linear Function

The y-intercept is the point where the line crosses the y-axis, given by the constant term b in the equation f(x) = mx + b. It represents the value of the function when x is zero, providing a starting point for graphing the line.

Graphing a Linear Function

Graphing involves plotting the y-intercept on the coordinate plane and using the slope to find another point by moving vertically and horizontally. Connecting these points with a straight line visually represents the function.