Graph a linear function with the given slope and y-intercept. slope: 5, y-intercept: 8
1 answer:
The graph of the linear function, y = 5x + 8, that has a slope of 5 and y-intercept of 8, is given in the graph below.
<h3>How to Plot the Graph of a Linear Function?</h3>A linear function can be expressed in the slope-intercept form as y = mx + b, given that:
- the value of m is the slope of the line = rise/run.
- the value of b is the y-intercept, which is the point where the line intersects the y-axis.
Given the following:
Slope (m) = 5 [this means the rise / run of the graph would be equal to 5]
Y-intercept (b) = 8 [this means the line will intersect the y-axis at point 8.
The equation of the linear function would be, y = 5x + 8.
Therefore, the graph of y = 5x + 8 is shown in the attachment below.
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Solution :
Given :
2y''' + 15y'' + 24y' + 11y= 0
Let x = independent variable
is a differential equation.
If
It is non homogeneous then,
The general solution = complementary solution + particular integral
If Q(x) = 0
It is called the homogeneous then the general solution = complementary solution.
2y''' + 15y'' + 24y' + 11y= 0
Auxiliary equation,
-1 | 2 15 24 11
<u> | 0 -2 - 13 -11 </u>
2 13 11 0
∴
The roots are
So,
Then the general solution is :