Question

Graph the function. $$ f(x)=-3 x+4 $$

Short answer

The graph of the function \(f(x)=-3x+4\) is a straight line that decreases, moving from left to right. It starts from the point (0,4) on the y-axis (y-intercept), and for each unit increase in \(x\), \(y\) decreases by 3 units (slope).

Step-by-step solution

Identify the slope and y-intercept

The function \(f(x)=-3x+4\) is in the slope-intercept form \(y=mx+b\), where \(m\) is the slope and \(b\) is the y-intercept. Here \(m=-3\) and \(b=4\). The slope tells us that for every unit increase in \(x\), \(y\) decreases by 3 units. The y-intercept tells us that when \(x=0\), \(y=4\).

Plot the y-intercept

The y-intercept is the point where the line crosses the y-axis. For this function, the y-intercept is \(4\). Plot this point on the y-axis.

Use the slope to find another point and plot it

Starting from the y-intercept, use the slope to find another point. The slope is -3, so move 1 unit to the right (increase in \(x\)) and 3 units down (decrease in \(y\)). Plot this point.

Draw the line

Draw a straight line that passes through the two points. This line represents the function \(f(x)=-3x+4\).