Question

1. graph the following lines using the x- and y-intercepts. a) 2x + y = 6

Explanation:

Step1: Find x - intercept

To find the x - intercept, set \(y = 0\) in the equation \(2x + y=6\).
Substitute \(y = 0\) into the equation: \(2x+0 = 6\), which simplifies to \(2x=6\).
Solve for \(x\) by dividing both sides by 2: \(x=\frac{6}{2}=3\). So the x - intercept is \((3,0)\).

Step2: Find y - intercept

To find the y - intercept, set \(x = 0\) in the equation \(2x + y = 6\).
Substitute \(x = 0\) into the equation: \(2(0)+y=6\), which simplifies to \(y = 6\). So the y - intercept is \((0,6)\).

Step3: Graph the line

Plot the points \((3,0)\) (on the x - axis) and \((0,6)\) (on the y - axis) on a coordinate plane. Then draw a straight line passing through these two points. This line represents the equation \(2x + y=6\).

Answer:

The x - intercept is \((3,0)\), the y - intercept is \((0,6)\), and the line is graphed by connecting these two points.