To find the slope of a line with two points, we need to find the slope. The slope is defined by the difference between y coordinates divided by the difference between x-coordinates.
For two points A and B:
[tex]\begin{gathered} \begin{cases}A(x_a,y_a) \\ B(x_b,y_b)\end{cases} \\ m=\frac{y_a-y_b}{x_a-x_b} \end{gathered}[/tex]
In this case, we can call A(0, 6) and B(7, 2)
Then we calculate:
[tex]m=\frac{6-2}{0-7}=-\frac{4}{7}[/tex]
Now that we know the slope, the equation of a line is:
[tex]\begin{gathered} \text{For a point }A(x_a.y_a) \\ y-y_a=m(x-x_a) \end{gathered}[/tex]
In this case, we know m and we can take A(0, 6):
[tex]\begin{gathered} y-6=-\frac{4}{7}(x-0) \\ y=-\frac{4}{7}x+6 \end{gathered}[/tex]
And that's the equation of the line.
