1. **State the problem:** Find the equation of the line in slope-intercept form $y=mx+b$ that passes through the points $(-2,-7)$ and $(3,8)$.\n\n2. **Formula for slope:** The slope $m$ is given by \n$$m=\frac{y_2 - y_1}{x_2 - x_1}$$\nwhere $(x_1,y_1)=(-2,-7)$ and $(x_2,y_2)=(3,8)$.\n\n3. **Calculate the slope:**\n$$m=\frac{8 - (-7)}{3 - (-2)}=\frac{8+7}{3+2}=\frac{15}{5}=3$$\n\n4. **Use slope-intercept form:**\n$$y=mx+b$$\nSubstitute $m=3$ and one point, say $(-2,-7)$, to find $b$.\n\n5. **Find $b$:**\n$$-7=3(-2)+b \implies -7 = -6 + b \implies b = -7 + 6 = -1$$\n\n6. **Write the final equation:**\n$$y=3x - 1$$\n\nThis is the equation of the line passing through the given points in slope-intercept form.