Find the equation of the line that passes through the points (2,3) and (4,7) using the slope-intercept form.
Answer
Therefore, the equation of the line that passes through the points (2,3) and (4,7) is \(y = 2x - 1\).
Step 1 ：First, we calculate the slope (m) of the line using the formula \(m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\). Substituting the given points, we get \(m = \frac{{7 - 3}}{{4 - 2}} = 2\).
Step 2 ：Next, we use the slope-intercept form of the line, which is \(y = mx + b\). Substituting the slope and one of the given points (2,3) into this equation, we get \(3 = 2*2 + b\), which simplifies to \(3 = 4 + b\). Solving for b gives us \(b = -1\).
Step 3 ：Therefore, the equation of the line that passes through the points (2,3) and (4,7) is \(y = 2x - 1\).
