Question

The table shows the height of a flower as it grows. What equation in slope-intercept form gives the flower's height at any time?
Time (weeks) Height (inches)
2                             12
4                             17
6                             22
8                             27

A. y = (5/2)x+7
B. y = (5/2)x+12
C. y = (5)x + 7
D. y= (5) x + 12

Answer 1

Use the table to draw the graph of height(y-axis) against week(x-axis).
The graph is a straight line. 
Find the gradient of the graph as the first step.
Gradient = (y2-y1)/(x2-x1)

              = (17-12)/(4-2)
              = 5/2
Use this gradient to find the equation of the line. Use one of the point from the table (e.g. (8,27)) and another general point (x,y).

∴5/2=(y-27)/(8-x)
   5/2 (x-8) = y-27
    (5/2)x - 20 = y-27
    
   y=(5/2)x - 20 + 27

  y = (5/2)x + 7

The answer is A
   

Answer 2

Answer:
y = $\frac{5}{2} x + 7$

Explanation:
The general form of the linear equation is:
y = mx + c
where:
m is the slope
c is the y-intercept

1- getting the slope:
slope can be calculated as follows:
m = $\frac{y2 - y1}{x2 - x1}$

I will use the points (2,12) and (8,27) to get the slope. You can choose any other two points and you will get the same answer.
m = $\frac{27-12}{8-2} = \frac{5}{2}$

The equation of the line now is:
y = $\frac{5}{2} x + c$

2- getting the y-intercept:
To get the y-intercept (c), we will use any of the given points, substitute in teh equation and solve for c.
I will use the point (6,22) as follows:
y = $\frac{5}{2} x + c$

22 = $\frac{5}{2} (6) + c$

22 = 15 + c
c = 7

Based on teh above, the equation of the line is:
y = $\frac{5}{2} x + 7$

Hope this helps :)