Question

Look at the cordinates below and write a linear equation (3,4) and (8,3)

Answer 1

Hello!

A linear equation has the form y = ax +b.

We also can call it the slope-intercept form.

We have two points, that I will name 1 and 2:

• (x1, y1) = (3, 4)

,

• (x2, y2) = (8, 3)

The first step is to find the slope (variable a). We must use the formula below:

$Slope=\frac{y_2-y_1}{x_2-x_1}$

So, let's replace it with the values that we know:

$Slope=\frac{3-4}{8-3}=-\frac{1}{5}$

Now we know variable a, we must find the variable b too. So, we can replace x and y in the equation with the coordinates of the point (x1, y1). Look:

$\begin{gathered} y=ax+b \\ 4=-\frac{1}{5}\cdot3+b \\ 4=-\frac{3}{5}+b \\ 4+\frac{3}{5}=b \\ b=\frac{23}{5} \end{gathered}$

So, the equation will be:

$\begin{gathered} y=ax+b \\ y=-\frac{1}{5}x+\frac{23}{5} \end{gathered}$

Look at the graph of this equation below: