Question

focus 1 here is a linear function: $y = 5x + 12$ a copy and complete this table of values. \

$$\begin{tabular}{|c|c|} \\hline x & y \\\\ \\hline -1 & \\\\ \\hline 0 & 12 \\\\ \\hline 1 & \\\\ \\hline 2 & \\\\ \\hline 3 & 27 \\\\ \\hline 4 & \\\\ \\hline \\end{tabular}$$

b work out where the graph of $y = 5x + 12$ crosses the $y$-axis. c show that $(5, 37)$ is on a graph of $y = 5x + 12$, but $(10, 74)$ is not on the graph.

Explanation:

Step1: Calculate y for x=-1

$y = 5(-1) + 12 = -5 + 12 = 7$

Step2: Calculate y for x=1

$y = 5(1) + 12 = 5 + 12 = 17$

Step3: Calculate y for x=2

$y = 5(2) + 12 = 10 + 12 = 22$

Step4: Calculate y for x=4

$y = 5(4) + 12 = 20 + 12 = 32$

Step5: Find y-axis intersection

Set $x=0$, $y = 5(0) + 12 = 12$

Step6: Verify (5,37)

Substitute $x=5$: $y=5(5)+12=25+12=37$

Step7: Verify (10,74)

Substitute $x=10$: $y=5(10)+12=50+12=62
eq 74$

Answer:

a. Completed table:

x	y
0	12
1	17
2	22
3	27
4	32

b. The graph crosses the y-axis at $(0, 12)$

c. For $(5, 37)$: $y=5(5)+12=37$, so it lies on the graph. For $(10, 74)$: $y=5(10)+12=62
eq74$, so it does not lie on the graph.