Question

Pleassse answer quick! (Again..)
Compare the function 3x+2y=12 to the following image.
Which of the following is a true statement?

A: The y-intercept of the graphed function is greater than the y-intercept of the function 3x+2y=12.
B: The x-intercept of the graphed function is greater than the x-intercept of the function 3x+2y=12.
C: The two functions have the same x-intercept.
D: The two functions have the same y-intercept.

Answer 1

Answer:

C) The two functions have the same x-intercept.

Step-by-step explanation:

The given function is

$3x+2y=12$

Let's analyse this function. We can its elements, that is, its slope and y-intercept points by isolating $y$, as follows

$3x+2y=12\\2y=12-3x\\y=\frac{12-3x}{2}\\ y=-\frac{3x}{2}+\frac{12}{2}\\ y=-\frac{3x}{2}+6$

So, the y-intercept is at $y=6$, which is not the same point showed in the graph. The slope of the linear equation is -3/2, which is not the same slope showed in the graph.

From the graph, we can deduct that te y-intercept is at $y=4$, and the slope is 1, because both variables increase at the same rate, which is 4 units, and if you divide 4/4 = 1.

At last, if we calculate the x-intecept of the linear equation, it would be

For $y=0$, let's find $x$

$3x+2y=12\\3x+2(0)=12\\x=\frac{12}{3}\\ x=4$

This means the x-intercept of the linear equation is at 4, and the graph shows the same x-intercept.

Therefore, the two functions have the same x-intercept. So, the right answer is C.

Answer 2

The only statement that is true of the given function and the graph is;

C: The two functions have the same x-intercept.

We are given the function;

3x + 2y = 12

Formula for equation of line in slope intercept form is y = mx + c.

Where m is slope and c is y-intercept

Thus, our equation can be expressed as;

y = -³/₂(x) + 6

Thus; slope = -³/₂ and y-intercept = 6

X-intercept is the point at which y = 0

Thus; 3x + 2(0) = 12

3x = 12

x = 12/3

x = 4

Option A; The y-intercept of the graph we are given is 4. This is lesser than that of the given function and as such the option is wrong.

Option B; The x-intercept of the given graph is 4 and that of the given function is 4 as well and so they are equal. Thus, this option is wrong

Option C; As seen in option B above they both have the same x-intercept. Thus, this statement is true.

Option D; They don't have the same y-intercept as shown in the values gotten earlier. Thus, this statement is false.

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