Questions: Graph using the slope and the y-intercept. y = -(1/4)x + 4 Use the graphing tool to graph the line. Use the slope and y-intercept when drawing the line.

Graph using the slope and the y-intercept.

y = -(1/4)x + 4

Use the graphing tool to graph the line. Use the slope and y-intercept when drawing the line.

Transcript text: Graph using the slope and the $y$-intercept. \[ y=-\frac{1}{4} x+4 \] Use the graphing tool to graph the line. Use the slope and $y$-intercept when drawing the line

Solution

Solution Steps

Step 1: Identify the slope and y-intercept

The given equation is $ y = -\frac{1}{4}x + 4 $. This is in the slope-intercept form $ y = mx + b $, where $ m $ is the slope and $ b $ is the y-intercept. Here, the slope $ m $ is $ -\frac{1}{4} $ and the y-intercept $ b $ is $ 4 $.

Step 2: Plot the y-intercept

The y-intercept is the point where the line crosses the y-axis. For the given equation, the y-intercept is $ 4 $. Plot the point $ (0, 4) $ on the graph.

Step 3: Use the slope to find another point

The slope $ -\frac{1}{4} $ means that for every 4 units you move to the right (positive direction on the x-axis), you move 1 unit down (negative direction on the y-axis). Starting from the y-intercept $ (0, 4) $, move 4 units to the right to $ (4, 4) $ and then 1 unit down to $ (4, 3) $. Plot the point $ (4, 3) $.