Given –9x2 + 4y2 – 18x + 16y – 29 ≤ 0, which graph represents the inequality?edge2021
2 answers:
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Answer:
a) P(0, <u>2</u>), Q(<u>4</u>, 0)
b) Please find attached the plot of the points P and Q on a chart made with MS Excel
c) Please find the graph of the line that represent the function 4·x + 2·y = 8 for values of x from -2 to 3 made with the Insert Chart feature on MS Excel
Step-by-step explanation:
The given equation for the line is 4·x + 2·y = 8
a) The coordinates of P = P(0, _)
Therefore, the point 'P', which is the point where the variable y = 0, is the point the (straight line) graph intercepts the x-axis (the x-intercept)
When y = 0 from the given equation, we get;
4·x + 2·y = 8
At the point y = 0;
4·x + 2 × 0 = 8
x = 8/4 = 2
x = 2
∴ The coordinates of P = P(0, _) = P(0, <u>2</u>)
Similarly, when x = 0, we get;
4·x + 2·y = 8
At the point x = 0;
4 × 0 + 2·y = 8
y = 8/2 = 4
y = 4
∴ The coordinates of Q = Q(_, 0) = Q(<u>4</u>, 0)
b) Rewriting the given equation in terms of 'y' gives;
y = (8 - 4·x)/2 = 4 - 2·x
y = 4 - 2·x
With the help of MS Excel, the points P and Q are plotted in the attached graph
c) The line of the graph of the function 4·x + 2·y = 8 for values of x from -2 to 3 can be added by Changing the Chart Type to 'Scatter with Smooth Lines and Markers' within MS Excel as presented in the included graph of the line.
