Question

graph the line.
y = -x + 4

Explanation:

Step1: Identify the slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For \(y=-x + 4\), the slope \(m=-1\) and the y - intercept \(b = 4\).

Step2: Plot the y - intercept

The y - intercept is \(4\), so we plot the point \((0,4)\) on the y - axis.

Step3: Use the slope to find another point

The slope \(m=-1=\frac{- 1}{1}\), which means we go down 1 unit and right 1 unit from the point \((0,4)\). So from \((0,4)\), moving down 1 and right 1 gives us the point \((1,3)\). We can also go up 1 unit and left 1 unit from \((0,4)\) to get \((-1,5)\) (since slope is also \(\frac{1}{-1}\)).

Step4: Draw the line

Connect the points \((0,4)\), \((1,3)\), \((-1,5)\) (and other points we can find using the slope) with a straight line.

(Note: Since the problem is about graphing, the final answer is the graph of the line \(y=-x + 4\) passing through points like \((0,4)\), \((1,3)\), \((-1,5)\) etc. on the given coordinate plane.)

Answer:

The line \(y = -x+4\) is graphed by plotting the y - intercept \((0,4)\) and using the slope \(-1\) to find other points (e.g., \((1,3)\), \((-1,5)\)) and then drawing a straight line through these points on the provided coordinate grid.