Find the equation of the line that passes through the points (2,3) and (4,7) using the slope-intercept form.
Answer
Step 4: Substitute b = -1 into the equation. The equation of the line is then \( y = 2x - 1 \).
Step 1 ：Step 1: Find the slope (m) of the line using the formula \( m = \frac{y2 - y1}{x2 - x1} \). Substituting the given points, we have \( m = \frac{7 - 3}{4 - 2} = 2 \).
Step 2 ：Step 2: Use the slope-intercept form of the equation of a line, \( y = mx + b \), where m is the slope and b is the y-intercept. From Step 1 we know that m = 2. We don't know b yet, so our equation is now \( y = 2x + b \).
Step 3 ：Step 3: Solve for b using one of the given points. Let's use (2,3). Substituting these values into the equation, we get \(3 = 2(2) + b \). Solving for b, we find that b = -1.
Step 4 ：Step 4: Substitute b = -1 into the equation. The equation of the line is then \( y = 2x - 1 \).
