Given the following function:
[tex]\text{ 3x - 2y = 16}[/tex]A.) SLOPE
Let's first transform the given equation into the standard slope-intercept form: y = mx + b
Because the m in the equation represents the value of the slope.
We get,
[tex]\begin{gathered} \text{ 3x - 2y = 16} \\ \text{ (3x - 2y = 16)( -}\frac{\text{ 1}}{\text{ 2}}) \\ \text{ -}\frac{3}{2}x\text{ + y = -}\frac{16}{2} \\ \text{ -}\frac{3}{2}x\text{ + y = -}8 \\ \text{ y = }\frac{3}{2}x\text{ - 8} \end{gathered}[/tex]The slope-intercept form of 3x - 2y = 16 is y = (3/2)x - 8. Where m = 3/2.
Therefore, the slope of the function is 3/2.
B.) Y - INTERCEPT
In the standard slope-intercept form : y = mx + b, b represents the y - intercept.
Therefore, in the converted form of the function y = (3/2)x - 8. b is equals to -8.
The y-intercept is 0, -8.
C.) X - INTERCEPT
The x - intercept is the point at y = 0.
We get,
[tex]\text{ 3x - 2y = 16}[/tex][tex]\text{ 3x - 2(0) = 16}[/tex][tex]\text{ 3x = 16}[/tex][tex]\text{ }\frac{\text{3x}}{3}\text{ = }\frac{\text{16}}{3}[/tex][tex]\text{ x = }\frac{\text{ 16}}{\text{ 3}}[/tex]Therefore, the x - intercept is 16/3, 0
D.) DOMAIN RANGE
The function has no undefined points nor domain constraints. Therefore, the domain is
[tex]-\infty\: We usually encounter undefined points when a given value of x will make the denominator equal to zero (0).Example: 2/(3 - x) at x = 3 is undefined.
E.) INCREASING OR DECREASING
The easiest way to determine if the function is decreasing or increasing is by looking at the slope (m). If the slope is greater than 0 (m > 0) or a positive, the function is increasing. If the slope is less than 0 (m < 0) or a negative, the function is decreasing.
Here, the slope is 3/2 which we first solved. Since the slope is greater than zero or a positive, the function is, therefore, increasing.
The answer is increasing.
