Draw the graph of linear equation 3x – 7y =21. Check whether (8, 1) is...
Graph of linear equation 3x – 7y =21
To graph the linear equation 3x – 7y = 21, we need to find at least two points on the line. We can do this by finding the x and y intercepts.
X-intercept: To find the x-intercept, we set y = 0 and solve for x.
3x – 7(0) = 21
3x = 21
x = 7
Therefore, the x-intercept is (7, 0).
Y-intercept: To find the y-intercept, we set x = 0 and solve for y.
3(0) – 7y = 21
-7y = 21
y = -3
Therefore, the y-intercept is (0, -3).
Now, we can plot these two points on a coordinate plane and draw a straight line passing through them.
Checking whether (8, 1) is a solution
To check whether (8, 1) is a solution of the given equation, we substitute x = 8 and y = 1 into the equation and see if it satisfies the equation.
3x – 7y = 21
3(8) – 7(1) = 24 – 7 = 17
Therefore, (8, 1) is NOT a solution of the given equation.
Explanation: The point (8, 1) does not lie on the line. We can see from the graph that the point (8, 1) is above the line. Therefore, it does not satisfy the equation.