Given two points, (3, 7) and (5,11), find the linear equation that passes through these two points.

Step 1 ：Step 1: Use the formula for the slope of a line, which is \(m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\). Substitute the given points into the formula to get \(m = \frac{{11 - 7}}{{5 - 3}}\).

Step 2 ：Step 2: Simplify the above expression to find the slope. \(m = \frac{4}{2}\).

Step 3 ：Step 3: Substitute the slope and one of the given points into the point-slope form of a linear equation, \(y - y_1 = m(x - x_1)\). Let's use point (3, 7), the equation becomes \(y - 7 = 2(x - 3)\).

Step 4 ：Step 4: Distribute and simplify the equation to put it in slope-intercept form (y = mx + b). The equation becomes \(y = 2x - 6 + 7\).

Step 5 ：Step 5: Simplify the equation further to get the final form, \(y = 2x + 1\).