Slope-intercept form of the line through $$$\left(1, 3\right)$$$ and $$$\left(10, 25\right)$$$

The slope of a line passing through two points $$$P = \left(x_{1}, y_{1}\right)$$$ and $$$Q = \left(x_{2}, y_{2}\right)$$$ is given by $$$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$$$.

We have that $$$x_{1} = 1$$$, $$$y_{1} = 3$$$, $$$x_{2} = 10$$$, and $$$y_{2} = 25$$$.

Plug the given values into the formula for a slope: $$$m = \frac{25 - 3}{10 - 1} = \frac{22}{9}$$$.

Now, the y-intercept is $$$b = y_{1} - m x_{1}$$$ (or $$$b = y_{2} - m x_{2}$$$, the result is the same):

$$$b = 3 - \left(\frac{22}{9}\right)\cdot \left(1\right) = \frac{5}{9}$$$

Finally, the equation of the line can be written in the form $$$y = b + m x$$$:

$$$y = \frac{22 x}{9} + \frac{5}{9}$$$

The slope of the line is $$$m = \frac{22}{9}\approx 2.444444444444444$$$A.

The y-intercept is $$$\left(0, \frac{5}{9}\right)\approx \left(0, 0.555555555555556\right)$$$A.

The x-intercept is $$$\left(- \frac{5}{22}, 0\right)\approx \left(-0.227272727272727, 0\right)$$$A.

The equation of the line in the slope-intercept form is $$$y = \frac{22 x}{9} + \frac{5}{9}\approx 2.444444444444444 x + 0.555555555555556$$$A.