Respuesta :
Since we have two points where the line passes through, first we need to find the slope between (4,6) and (5,9)
For that, we label the coordinates as:
[tex]\begin{gathered} x_1=4 \\ y_1=6 \\ x_2=5 \\ y_2=9 \end{gathered}[/tex]And we use the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Substituting the values:
[tex]\begin{gathered} m=\frac{9-6}{5-4} \\ m=\frac{3}{1} \\ m=3 \end{gathered}[/tex]Now that we have the slope, we use the point slope equation:
[tex]y=m(x-x_1)+y_1[/tex]And we substitute the known values including the slope:
[tex]\begin{gathered} y=3(x-4)+6 \\ \end{gathered}[/tex]This is the equation in point slope form, if you need the slope intercept form (the simplified form) we do the following...
We use the distributive property to multiply 3 by x and 3 by -4:
[tex]\begin{gathered} y=3x-12+6 \\ y=3x-6 \end{gathered}[/tex]Answer: the equation of the line in point slople form is
[tex]y=3(x-4)+6[/tex]And the simplified form is
[tex]y=3x-6[/tex]