Question

Write an equation for the function that passes through the points 1, 3/2 and 3/2, 2

Answer 1

The equation for the function is $y=x+\frac{1}{2}$

Explanation:

The equation for the function that passes through the points $\left(1, \frac{3}{2}\right)$ and $\left(\frac{3}{2}, 2\right)$

The equation of the line that passes through the points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ is given by

$y-y_{1}=m\left(x-x_{1}\right)$

where m is the slope and it can be determined using the formula,

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substituting the values of x and y in the slope formula, we have,

$m=\left(\frac{2-\frac{3}{2}}{\frac{3}{2}-1}\right)$

Simplifying, we get,

$\begin{aligned}&m=\frac{\left(\frac{1}{2}\right)}{\left(\frac{1}{2}\right)}\\&m=1\end{aligned}$

Thus, the slope is m=1.

Substituting the values in the equation $y-y_{1}=m\left(x-x_{1}\right)$, we have,

$y-\frac{3}{2} =1(x-1)$

Multiplying the terms within the bracket,

$y-\frac{3}{2} =x-1$

Adding $\frac{3}{2}$ on both sides of the equation,

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

Thus, the equation for the function is $y=x+\frac{1}{2}$