Slope-intercept form of the line through $$$\left(-1, 7\right)$$$ and $$$\left(3, -4\right)$$$

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 $$$x_{1} = -1$$$, $$$y_{1} = 7$$$, $$$x_{2} = 3$$$, and $$$y_{2} = -4$$$.

Plug the given values into the formula for a slope: $$$m = \frac{-4 - 7}{3 - \left(-1\right)} = - \frac{11}{4}$$$.

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

$$$b = 7 - \left(- \frac{11}{4}\right)\cdot \left(-1\right) = \frac{17}{4}$$$

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

$$$y = \frac{17}{4} - \frac{11 x}{4}$$$

The slope of the line is $$$m = - \frac{11}{4} = -2.75$$$A.

The y-intercept is $$$\left(0, \frac{17}{4}\right) = \left(0, 4.25\right)$$$A.

The x-intercept is $$$\left(\frac{17}{11}, 0\right)\approx \left(1.545454545454545, 0\right)$$$A.

The equation of the line in the slope-intercept form is $$$y = \frac{17}{4} - \frac{11 x}{4} = 4.25 - 2.75 x$$$A.