Answer:
See attached photo
Step-by-step explanation:
To sketch the line defined by the linear equation (2x + 3y - 21 = 0), you need to find the x- and y-intercepts. These intercepts occur where the line crosses the x-axis and y-axis, respectively.
Finding the x-intercept:
The x-intercept occurs where (y = 0). To find it, set (y = 0) in the equation and solve for (x):
[tex](2x + 3(0) - 21 = 0)[/tex]
[tex](2x - 21 = 0)[/tex]
[tex](2x = 21)[/tex]
[tex](x = \frac{21}{2})[/tex]
[tex](x = 10.5)[/tex]
So, the x-intercept is at the point ((10.5, 0)).
Finding the y-intercept:
The y-intercept occurs where (x = 0). To find it, set (x = 0) in the equation and solve for (y):
[tex](2(0) + 3y - 21 = 0)[/tex]
[tex](3y - 21 = 0)[/tex]
[tex](3y = 21)[/tex]
[tex](y = \frac{21}{3})[/tex]
[tex](y = 7)[/tex]
So, the y-intercept is at the point ((0, 7)).
Sketching the Line:
Now, plot the x-intercept (10.5, 0) and the y-intercept (0, 7) on a coordinate plane. Draw a straight line through these two points, and this line is the graph of the linear equation (2x + 3y - 21 = 0).
Hope this helps!
