Question

hat is the graph of the equation ( y = -\frac{1}{4}x + 2 )?
the y - intercept is, which means the line crosses the y - axis at the point
(type integers or fractions. simplify your answers.)
the slope of the line is negative, so it goes from left to right.
start at the y - intercept. move down, and then move right. you are now at the point
(type integers or fractions. simplify your answers.)
plot both points. then, draw a line to connect the two points. choose the correct graph below.

Explanation:

Step1: Find the y - intercept

The equation of a line is in the form \(y = mx + b\), where \(b\) is the y - intercept. For the equation \(y=-\frac{1}{4}x + 2\), when \(x = 0\), \(y=2\). So the y - intercept is \(2\), and the line crosses the y - axis at the point \((0,2)\).

Step2: Analyze the slope

The slope \(m=-\frac{1}{4}\). A negative slope means the line goes down from left to right.

Step3: Use the slope to find another point

Starting from the y - intercept \((0,2)\), using the slope \(m =-\frac{1}{4}=\frac{\text{change in }y}{\text{change in }x}\). The change in \(y\) (vertical change) is \(- 1\) (move down \(1\)) and the change in \(x\) (horizontal change) is \(4\) (move right \(4\)). So from the point \((0,2)\), moving down \(1\) and right \(4\) gives the point \((4,1)\).

Answer:

The y - intercept is \(2\), which means the line crosses the y - axis at the point \((0,2)\). The slope of the line is negative, so it goes down from left to right. Start at the y - intercept. Move down \(1\) and then move right \(4\). You are now at the point \((4,1)\).