Question

graph this line using the slope and y - intercept:

$y = - \frac{1}{4}x + 1$

click to select points on the graph.

Explanation:

Step1: Identify the \( y \)-intercept

The equation is in slope - intercept form \( y=mx + b \), where \( b = 1 \). So, the \( y \)-intercept is at the point \( (0,1) \).

Step2: Use the slope to find another point

The slope \( m=-\frac{1}{4}=\frac{\Delta y}{\Delta x} \). Starting from \( (0,1) \), if \( \Delta x = 4 \) (move 4 units to the right), then \( \Delta y=- 1 \) (move 1 unit down). So, the new point is \( (0 + 4,1-1)=(4,0) \).

Step3: Draw the line

Connect the points \( (0,1) \) and \( (4,0) \) with a straight line. This line represents the equation \( y = -\frac{1}{4}x + 1 \).

Answer:

To graph the line \( y = -\frac{1}{4}x + 1 \), first plot the \( y \)-intercept at \( (0,1) \). Then, use the slope \( -\frac{1}{4} \) (which means for every 4 units you move to the right along the \( x \)-axis, you move 1 unit down along the \( y \)-axis) to find another point. For example, from \( (0,1) \), moving 4 units right (to \( x = 4 \)) and 1 unit down gives the point \( (4,0) \). Connect these two points with a straight line.