Problem

If a line passes through the points (4,7) and (2,3), find the equation of the line using the slope-intercept formula.

Answer

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Answer

Step 3: Now we have the slope and the y-intercept, we can write down the equation of the line as \( y = -2x + 15 \)

Steps

Step 1 ：Step 1: First, let's find the slope (m) of the line using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \) . So, \( m = \frac{3 - 7}{2 - 4} = -2 \)

Step 2 ：Step 2: Now, let's use the slope-intercept form of the line, which is \( y = mx + b \) . We know the slope (m) and we can use one of the points (4,7) to solve for b. So, \( 7 = -2 * 4 + b \) ,\( b = 7 + 8 = 15 \)

Step 3 ：Step 3: Now we have the slope and the y-intercept, we can write down the equation of the line as \( y = -2x + 15 \)

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