To graph these linear equations, we need to find at least two points that lie on each line. The easiest way is to find the x-intercept and y-intercept for each equation.
Equation 1: x + y = 4
- Find x-intercept: Set y = 0 → x + 0 = 4 → x = 4 → Point: (4, 0)
- Find y-intercept: Set x = 0 → 0 + y = 4 → y = 4 → Point: (0, 4)
- Plot these two points and draw a straight line through them.
Equation 2: 2x + 4y = 8
- Simplify first: Divide everything by 2 → x + 2y = 4
- Find x-intercept: Set y = 0 → x + 0 = 4 → x = 4 → Point: (4, 0)
- Find y-intercept: Set x = 0 → 0 + 2y = 4 → y = 2 → Point: (0, 2)
- Plot these two points and draw a straight line through them.
Equation 3: 3x - ½y = 2
- To make it easier, multiply everything by 2 to eliminate the fraction: 6x - y = 4
- Find x-intercept: Set y = 0 → 6x = 4 → x = 4/6 = 2/3 → Point: (2/3, 0)
- Find y-intercept: Set x = 0 → -y = 4 → y = -4 → Point: (0, -4)
- Plot these two points and draw a straight line through them.
Equation 4: y = 3x + 2
- This is already in slope-intercept form (y = mx + b), where b = 2 is the y-intercept.
- Find y-intercept: When x = 0, y = 2 → Point: (0, 2)
- Find another point: Let x = 1 → y = 3(1) + 2 = 5 → Point: (1, 5)
- Plot these two points and draw a straight line through them.
Equation 5: x - y = 5
- Find x-intercept: Set y = 0 → x - 0 = 5 → x = 5 → Point: (5, 0)
- Find y-intercept: Set x = 0 → 0 - y = 5 → y = -5 → Point: (0, -5)
- Plot these two points and draw a straight line through them.
Equation 6: y = -⅔x + 4
- This is in slope-intercept form, where b = 4 is the y-intercept.
- Find y-intercept: When x = 0, y = 4 → Point: (0, 4)
- Find another point: Let x = 3 → y = -⅔(3) + 4 = -2 + 4 = 2 → Point: (3, 2)
- Plot these two points and draw a straight line through them.
Final Answer:
For each equation, plot the two intercept points found above and draw a straight line connecting them. Label each line with its corresponding equation number or equation itself as instructed.
Parent Tip: Review the logic above to help your child master the concept of graphing linear tables worksheet.
