Question

Write an equation for the function that includes the points.(-2, 3/5) and (-1,2)

Answer 1

The equation of a line is y = mx + c

m =slope

$m\text{ = }\frac{y_2-y_1}{x_2-x_1}$

c = intercept

y2 = 2, y1 = 2/5, x2 = -1, x1 =-2

$\begin{gathered} m\text{ =}\frac{2\text{ - }\frac{2}{5}}{-1\text{ - (-2)}} \\ m\text{ = 1}.6 \end{gathered}$

using any two corresponding points of x and y say x2 = -1 and y2=2 we can substitute into the equation of a line and find c, the intercept

y = mx +c

2 = 1.6(-1) +c

2 = -1.6 +c

2 +1.6 =c

c = 3.6

Equation of the functions therefore is

y = 1.6x + 3.6

The answer is y= 10 * 5^x

That is option C

Because if x= - 2

y = 10 x 5 ^-2 = 10 x 0.04 = 0.4

That is equal to the value of y= 2/5 at x = -2