Problem

Find the equation of the line that passes through the points (2,3) and (4,7) using the slope-intercept form.

Answer

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Answer

Step 4: Substitute b = -1 into the equation. The equation of the line is then y=2x−1.

Steps

Step 1 ：Step 1: Find the slope (m) of the line using the formula m=y2−y1x2−x1. Substituting the given points, we have m=7−34−2=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.

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