Given the linear equations:
• x - 2y = 2
,
• 3x + 3y = 7
,
• 7x - y = 21
,
• 3x - 5y = 20
Let's match the linear equations with their x- and y-intercepts.
The x-intercept is the point the line crosses the x-axis. Here, the y-value is zero,
The y-intercept is the point the line crosses the y-axis. Here, the x-value is zero.
To find the x-intercept, plug in 0 for y and solve for x.
To find the y-intercept, plug in 0 for x and solve for y.
• Equation 1: x - 2y = 2
To find the x-intercept, plug in 0 for y and solve for x:
x - 2(0) = 2
x = 2
Therefore, the x-intercept is: (2, 0)
To find the y-intercept, plug in 0 for x and solve for y:
0 - 2y = 2
-2y = 2
y = -2/2
y = -1
Therefore, the y-intercept is (0, -1)
For equation 1, we have the x- and y-intercepts:
(2, 0) and (0, -1)
• Equation 2: -3x + 3y = 7
x-intercept:
-3x + 3(0) = 7
-3x = 7
x = -7/3
Therefore, the x-intercept is (-7/3, 0)
y-intercept:
-3(0) + 3y = 7
3y = 7
y = 7/3
Therefore, the y-intercept is (0, 7/3)
• Equation 3: 7x - y = 21
x-intercept:
7x - 0 = 21
7x = 21
x = 21/7
x = 3
Therefore, the x-intercept is (3, 0)
y-intercept:
7(0) - y = 21
-y = 21
y = -21
Therefore, the y-intercept is (0, -21)
• Equation 4: 3x - 5y = -20
x-intercept:
3x - 5(0) = -20
3x = -20
x = -20/3
Therefore, the x-intercept is (-20/3, 0)
y-intercept:
3(0) - 5y = -20
-5y = -20
y = -20/-5
y = 4
Therefore, the y-intercept is (0, 4)
• ANSWER:
,
• x - 2y = 2 ===> (2, 0) and (0, -1)
• -3x + 3y = 7 ===> (-7/3, 0) and (0, 7/3)
• 7x - y = 21 ===> (3, 0) and (0, -21)
• 3x - 5y ===> (-20/3, 0) and (0, 4)