Question

(5) 2x + y = 4
(6) x + y = -4

Explanation:

Step1: Rewrite the equation in slope-intercept form

For the equation \(2x + y = 4\), we can rewrite it as \(y=-2x + 4\). This is in the form \(y = mx + b\), where the slope \(m=-2\) and the y - intercept \(b = 4\). To find two points on the line, when \(x = 0\), \(y=4\) (the y - intercept). When \(y = 0\), we solve \(0=-2x + 4\), which gives \(2x=4\) or \(x = 2\). So the points \((0,4)\) and \((2,0)\) are on the line.

Step2: Plot the points and draw the line

On the given grid, find the point \((0,4)\) (on the y - axis, 4 units up from the origin) and the point \((2,0)\) (on the x - axis, 2 units to the right of the origin). Then draw a straight line passing through these two points.

Step3: For the equation \(x + y=-4\)

Rewrite it in slope - intercept form: \(y=-x - 4\). The slope \(m=-1\) and the y - intercept \(b=-4\). When \(x = 0\), \(y=-4\) (on the y - axis, 4 units down from the origin). When \(y = 0\), we solve \(0=-x - 4\), which gives \(x=-4\) (on the x - axis, 4 units to the left of the origin). So the points \((0,-4)\) and \((-4,0)\) are on the line.

Step4: Plot the points and draw the line

On the given grid, find the point \((0,-4)\) (on the y - axis, 4 units down from the origin) and the point \((-4,0)\) (on the x - axis, 4 units to the left of the origin). Then draw a straight line passing through these two points.

Answer:

For \(2x + y = 4\), plot \((0,4)\) and \((2,0)\) and draw the line. For \(x + y=-4\), plot \((0,-4)\) and \((-4,0)\) and draw the line.