Question

Please help me solve question 7 on my algebra homework

Answer 1

To graph this linear function, we can use the x- and the y-intercepts of the function. To achieve this, we can proceed as follows:

1. Finding the x-intercept of the line

The x-intercept is the point where the function passes through the x-axis and at this point the value for y = 0. Then, the x-intercept is:

$3x-2y=-12\Rightarrow y=0\Rightarrow3x-2(0)=-12$

Then, we have:

$3x=-12\Rightarrow\frac{3x}{3}=-\frac{12}{3}\Rightarrow x=-4$

Then, the x-intercept is (-4, 0). See that it is easier to identify this point on the coordinate to graph the function.

2. Finding the y-intercept

In this case, we need to find the value of y when x = 0. The y-intercept is the point where the linear function passes through the y-axis. Then, we have:

$3x-2y=-12\Rightarrow x=0\Rightarrow3(0)-2y=-12$

Then, we can divide both sides of the equation by -2:

$-2y=-12\Rightarrow-\frac{2y}{-2}=-\frac{12}{-2}\Rightarrow y=6$

Then, the y-intercept is (0, 6).

3. Finding the slope of the line

We can rewrite the line equation given in the standard form into the slope-intercept form as follows:

The slope-intercept form of the line is:

$y=mx+b$

Where

• m is the slope of a line.

,

• b is the y-intercept of the line.

Then, we have:

$3x-2y=-12$

To solve the equation for y, we can follow the next steps:

1. Subtract 3x to both sides of the equation:

$3x-3x-2y=-12-3x\Rightarrow-2y=-12-3x$

2. Divide both sides of the equation by -2:

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

Then, the slope of this line is m = 3/2.

With all of this information, we can answer the question about the attributes:

1. Domain

The domain of the function is, in interval form, as (-∞, ∞). That is the values for x are for all the values of x.

2. Range

The range of the linear function is for values of y from -∞ to ∞, or in interval form as (-∞, ∞).

We can see this if we graph the function as follows (we can graph the function by using the intercepts we found above):

3. Zero

The zero of the function is the point for which the function is equal to zero, and we found that this point is the same as the x-intercept. The zero of the function is x = -4, because:

$f(-4)=\frac{3}{2}(-4)+6=3(-2)+6=-6+6=0$

4. The Y-intercept

We already found that the y-intercept is (0, 6).

5. The slope of the line

We already found the slope of the line: m = 3/2.

6. Type of slope

The slope of the line is a positive slope.

7. The value of the linear function when f(0)

To find this value, we need to substitute the value of x = 0 into the line equation as follows (the result will be the y-intercept):

$y=f(x)=\frac{3}{2}x+6\Rightarrow f(0)=\frac{3}{2}(0)+6\Rightarrow f(0)=6$

Then, f(0) = 6.

8. The value of x, where f(x) = 0

We already found this value. The value of x for which the function is zero is x = -4 (see above).

Therefore, in summary, we have: