Question

6 which correctly describes the graph below? a. non - linear; not a function b. non - linear; function c. linear; function d. linear; not a function 7 the graph of a linear relationship contains the points (1, 10) and (3, 16). write the equation of the line in slope - intercept form. 8 the graph of a linear relationship contains the points (0, 3) and (6, 0). which is a true statement about the line? a. the y - intercept is 3. b. the slope of the line is \\(\frac{1}{2}\\) c. the equation of the line is \\(y = \frac{1}{2}x - 3\\) d. all of the above are true. 9 which of the following equations represents a linear function? a. \\(y = \frac{15}{x}\\) b. \\(y = 2x^3 + 2\\) c. \\(y = \frac{1}{2}x + 4\\) d. \\(y = x^2\\) 10 which table represents a linear relationship? a \\(\

$$\begin{array}{|c|c|c|c|c|} \\hline x & - 2 & - 1 & 0 & 1 \\\\ \\hline y & 20 & 5 & 0 & 5 \\\\ \\hline \\end{array}$$

\\) b \\(\

$$\begin{array}{|c|c|c|c|c|} \\hline x & - 2 & - 1 & 0 & 1 \\\\ \\hline y & 9.4 & 6.2 & 3 & - 0.2 \\\\ \\hline \\end{array}$$

\\) a. table a only b. table b only c. both tables d. neither table

Explanation:

Question 6

Step1: Check linearity

The graph is a curve, not a straight line, so it is non-linear.

Step2: Check function (Vertical Line Test)

Any vertical line intersects the graph at most once, so it is a function.

Step1: Calculate slope

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$. Use points $(1,10)$ and $(3,16)$:
$m=\frac{16-10}{3-1}=\frac{6}{2}=3$

Step2: Find y-intercept

Use slope-intercept form $y=mx+b$, substitute $m=3$, $x=1$, $y=10$:
$10=3(1)+b \implies b=10-3=7$

Step3: Write final equation

Combine slope and intercept into $y=mx+b$.

Step1: Identify y-intercept

The point $(0,3)$ means the y-intercept $b=3$, so statement A is true.

Step2: Calculate slope

Use points $(0,3)$ and $(6,0)$: $m=\frac{0-3}{6-0}=-\frac{1}{2}$, so statement B is false.

Step3: Verify line equation

Using $m=-\frac{1}{2}$ and $b=3$, the equation is $y=-\frac{1}{2}x+3$, so statement C is false.

Answer:

B. Non-linear; function

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Question 7