Find an equation of the line that passes through the two given points. Write the equation in slope-intercept form, if possible. passes through $(1,7)$ and $(-2,1)$

Step 1 ：Understand the problem: We are asked to find the equation of a line that passes through two given points. The equation of a line is typically written in the form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Step 2 ：Find the slope: The slope of a line passing through two points \((x1, y1)\) and \((x2, y2)\) is given by the formula: \(m = \frac{(y2 - y1)}{(x2 - x1)}\). Substituting the given points into this formula, we get: \(m = \frac{(1 - 7)}{(-2 - 1)} = \frac{-6}{-3} = 2\).

Step 3 ：Find the y-intercept: We can find the y-intercept by substituting one of the points and the slope into the equation \(y = mx + b\) and solving for \(b\). Using the point \((1, 7)\), we get: \(7 = 2*1 + b\), \(7 = 2 + b\), \(b = 7 - 2 = 5\).

Step 4 ：Write the equation: Substituting the slope and y-intercept into the equation \(y = mx + b\), we get: \(y = 2x + 5\).

Step 5 ：Check the solution: Substitute the coordinates of the two points into the equation to verify that they satisfy the equation. For \((1,7)\): \(7 = 2*1 + 5 = 7\). For \((-2,1)\): \(1 = 2*(-2) + 5 = 1\). Both points satisfy the equation, so the equation \(y = 2x + 5\) is the line that passes through the points \((1,7)\) and \((-2,1)\).

Step 6 ：\(\boxed{y = 2x + 5}\) is the final answer.