Question

module 11 (linear equations) assignment
score: 6/20 answered: 6/20
question 7
sketch a graph of the linear equation.
-x - 4y = -8
clear all draw:
submit question

Explanation:

Step1: Rewrite in slope - intercept form

We start with the equation \(-x - 4y=-8\). We want to solve for \(y\) to get it in the form \(y = mx + b\) (where \(m\) is the slope and \(b\) is the \(y\) - intercept).
First, add \(x\) to both sides of the equation:
\(-4y=x - 8\)
Then, divide each term by \(-4\):
\(y=-\frac{1}{4}x + 2\)

Step2: Find the \(y\) - intercept

The \(y\) - intercept occurs when \(x = 0\). Substitute \(x = 0\) into the equation \(y=-\frac{1}{4}x + 2\):
\(y=-\frac{1}{4}(0)+2=2\). So the \(y\) - intercept is the point \((0,2)\).

Step3: Find another point (using the slope)

The slope \(m =-\frac{1}{4}\), which can be thought of as \(\frac{\text{rise}}{\text{run}}=\frac{- 1}{4}\).
Starting from the point \((0,2)\) (the \(y\) - intercept), we move down 1 unit (because the rise is - 1) and then move 4 units to the right (because the run is 4).
So the new point is \((0 + 4,2-1)=(4,1)\). We could also move up 1 unit and left 4 units from \((0,2)\) to get the point \((0 - 4,2 + 1)=(-4,3)\).

Step4: Sketch the graph

Plot the points \((0,2)\), \((4,1)\) (or other points we found) on the coordinate plane and then draw a straight line through them.

To sketch the graph of \(-x - 4y=-8\) (or \(y =-\frac{1}{4}x + 2\)):

• Plot the \(y\) - intercept \((0,2)\).
• Use the slope \(-\frac{1}{4}\) to find another point (e.g., from \((0,2)\), move 4 units right and 1 unit down to get \((4,1)\)).
• Draw a straight line through the plotted points.

(Note: Since the problem asks to sketch the graph, the key is to identify the \(y\) - intercept and a second point using the slope to draw the line. The final answer in terms of the graph - sketching process is to plot the points and draw the line as described.)

Answer:

Step1: Rewrite in slope - intercept form

We start with the equation \(-x - 4y=-8\). We want to solve for \(y\) to get it in the form \(y = mx + b\) (where \(m\) is the slope and \(b\) is the \(y\) - intercept).
First, add \(x\) to both sides of the equation:
\(-4y=x - 8\)
Then, divide each term by \(-4\):
\(y=-\frac{1}{4}x + 2\)

Step2: Find the \(y\) - intercept

The \(y\) - intercept occurs when \(x = 0\). Substitute \(x = 0\) into the equation \(y=-\frac{1}{4}x + 2\):
\(y=-\frac{1}{4}(0)+2=2\). So the \(y\) - intercept is the point \((0,2)\).

Step3: Find another point (using the slope)

The slope \(m =-\frac{1}{4}\), which can be thought of as \(\frac{\text{rise}}{\text{run}}=\frac{- 1}{4}\).
Starting from the point \((0,2)\) (the \(y\) - intercept), we move down 1 unit (because the rise is - 1) and then move 4 units to the right (because the run is 4).
So the new point is \((0 + 4,2-1)=(4,1)\). We could also move up 1 unit and left 4 units from \((0,2)\) to get the point \((0 - 4,2 + 1)=(-4,3)\).

Step4: Sketch the graph

Plot the points \((0,2)\), \((4,1)\) (or other points we found) on the coordinate plane and then draw a straight line through them.

To sketch the graph of \(-x - 4y=-8\) (or \(y =-\frac{1}{4}x + 2\)):

• Plot the \(y\) - intercept \((0,2)\).
• Use the slope \(-\frac{1}{4}\) to find another point (e.g., from \((0,2)\), move 4 units right and 1 unit down to get \((4,1)\)).
• Draw a straight line through the plotted points.

(Note: Since the problem asks to sketch the graph, the key is to identify the \(y\) - intercept and a second point using the slope to draw the line. The final answer in terms of the graph - sketching process is to plot the points and draw the line as described.)