First, let's find the slope of the line using the formula [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points on the line.
The equation for the slope of this line would be:
[tex]\dfrac{\frac{7}{5} - \frac{6}{5}}{-\frac{3}{5} - \frac{2}{5}} = \dfrac{\frac{1}{5}}{-1} = -\dfrac{1}{5}[/tex]
Now, let's find use the point-slope equation to find an equation for our line, which is [tex](y - y_1) = m(x - x_1)[/tex], where [tex](x_1, y_1)[/tex] is a point on the line and [tex]m[/tex] is the slope. The point-slope equation for our line would be:
[tex](y - \frac{6}{5}) = -\frac{1}{5}(x - \frac{2}{5})[/tex]
[tex]y - \frac{6}{5} = -\frac{1}{5}x + \frac{2}{25}[/tex]
[tex]y = -\frac{1}{5}x + \frac{32}{25}[/tex]
The slope-intercept form of the line would be y = -x/5 + 32/25.
Now, we can use operations to convert this equation into standard form:
[tex]25y = -5x + 32[/tex]
[tex]5x + 25y = 32[/tex]
The standard form of the line would be 5x + 25y = 32.
