Question

(3) 4x - y = 6

Explanation:

Step1: Rewrite in slope - intercept form

We start with the equation \(4x - y=6\). 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).
Subtract \(4x\) from both sides: \(-y=-4x + 6\).
Multiply both sides by \(- 1\) to get \(y = 4x-6\).

Step2: Find the \(y\) - intercept

The \(y\) - intercept (\(b\)) is the value of \(y\) when \(x = 0\). Substitute \(x = 0\) into \(y=4x - 6\).
\(y=4(0)-6=-6\). So the point \((0,-6)\) is on the line.

Step3: Find another point using the slope

The slope \(m = 4=\frac{4}{1}\), which means for every increase of \(1\) in \(x\), \(y\) increases by \(4\).
Starting from the \(y\) - intercept \((0,-6)\), if we increase \(x\) by \(1\) (let \(x = 1\)), then \(y=4(1)-6=-2\). So the point \((1, - 2)\) is also on the line.

Step4: Plot the points and draw the line

Plot the points \((0,-6)\) and \((1,-2)\) on the coordinate grid. Then draw a straight line passing through these two points. The line should have a slope of \(4\) (steeply rising) and cross the \(y\) - axis at \((0,-6)\).

Answer:

To graph \(4x - y = 6\) (or \(y = 4x-6\)):

1. Plot the \(y\) - intercept \((0,-6)\).
2. Use the slope \(m = 4\) to find a second point (e.g., from \((0,-6)\), move \(1\) unit right and \(4\) units up to \((1,-2)\)).
3. Draw a straight line through the two points.