Problem

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

Answer

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Answer

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

Steps

Step 1 ：Step 1: Use the formula for the slope of a line, which is m=y2−y1x2−x1. Substitute the given points into the formula to get m=11−75−3.

Step 2 ：Step 2: Simplify the above expression to find the slope. m=42.

Step 3 ：Step 3: Substitute the slope and one of the given points into the point-slope form of a linear equation, y−y1=m(x−x1). 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.

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