Question

The graph of a function is a line that passes through the coordinates (2, 11) and (8, 14).Part AWhich shows how to find the rate of change for the function?A.$\frac{8 - 2}{14 - 11}$B.$\frac{14 - 11}{8 - 2}$C.$\frac{14 - 8}{11 - 2}$D.$\frac{11 - 2}{14 - 8}$Part BWhich is an equation in terms of x and y for this function?A.$y = \frac{1}{2} x + 10$B.$y = \frac{2}{3} x + 9$C.$y = \frac{3}{2} x + 8$D.$y = 2x + 7$

Answer 1

The slope of a line is defined as rise/run. In other words, it is the change in the y-coordinate over the change in x-coordinate.

Now, for the points (2, 11) and (8, 14) the change in y-coordinate is

$14-11$

and the change in the x-coordinate is

$8-2$

Therefore, the slope is

$\frac{14-11}{8-2}$

which is choice B.

Part B.

The equation of a line is of the form

$y=mx+b$

where m is the slope and b is the y-intercept.

Now, the slope we found from part A is

$m=\frac{14-11}{8-2}=\frac{3}{6}=\frac{1}{2}$

Therefore,

$y=\frac{1}{2}x+b$

we now just need to find b.

We find the y-intercept b using the point (2. 11) and putting in y =11 and x = 2 in the above equation gives

$11=\frac{1}{2}(2)+b$$11=1+b$$\therefore b=10$

Hence, the equation of the line is

$y=\frac{1}{2}x+10$

which is choice A,