Question

additional practice
2.9 ap 1
what is the graph of the equation $y = -\frac{1}{4}x + 2$?

the y - intercept is 2, which means the line crosses the y - axis at the point (0, 2).
(type integers or fractions. simplify your answers.)
the slope of the line is negative, so it goes down from left to right.
start at the y - intercept. move down \\(\square\\), and then move right \\(\square\\). you are now at the point (\\(\square\\),
(type integers or fractions. simplify your answers.)

Explanation:

Step1: Analyze the slope - intercept form

The equation of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. For \(y=-\frac{1}{4}x + 2\), \(m=-\frac{1}{4}\) and \(b = 2\).

Step2: Use the slope to find another point

The slope \(m=\frac{\text{rise}}{\text{run}}\). Since \(m =-\frac{1}{4}\), the rise is \(- 1\) (move down \(1\)) and the run is \(4\) (move right \(4\)).
Starting from the \(y\) - intercept \((0,2)\), if we move down \(1\) (the \(y\) - coordinate becomes \(2-1 = 1\)) and move right \(4\) (the \(x\) - coordinate becomes \(0 + 4=4\)), we get to the point \((4,1)\).

Answer:

Move down \(1\), and then move right \(4\). You are now at the point \((4,1)\)