Slope-intercept form of the line through $\left(-3, 3\right)$ and $\left(18, 26\right)$

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 $x_{1} = -3$, $y_{1} = 3$, $x_{2} = 18$, and $y_{2} = 26$.

Plug the given values into the formula for a slope: $m = \frac{26 - 3}{18 - \left(-3\right)} = \frac{23}{21}$.

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

$b = 3 - \left(\frac{23}{21}\right)\cdot \left(-3\right) = \frac{44}{7}$

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

$y = \frac{23 x}{21} + \frac{44}{7}$

The slope of the line is $m = \frac{23}{21}\approx 1.095238095238095$A.

The y-intercept is $\left(0, \frac{44}{7}\right)\approx \left(0, 6.285714285714286\right)$A.

The x-intercept is $\left(- \frac{132}{23}, 0\right)\approx \left(-5.739130434782609, 0\right)$A.

The equation of the line in the slope-intercept form is $y = \frac{23 x}{21} + \frac{44}{7}\approx 1.095238095238095 x + 6.285714285714286$A.