Parsons John
12/10/2023 · Middle School

Write the equation of a line in slope-intercept form that passes through the point (1, 2) with a slope of 3.

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To write the equation of a line in slope-intercept form, which is given by the formula: \[ y = mx + b \] where \( m \) is the slope and \( b \) is the y-intercept, we can use the given slope and the point through which the line passes. Given: - Slope (\( m \)) = 3 - Point = (1, 2) We can substitute the slope and the coordinates of the point into the equation to find \( b \): 1. Substitute \( m = 3 \), \( x = 1 \), and \( y = 2 \) into the equation: \[ 2 = 3(1) + b \] 2. Simplify the equation: \[ 2 = 3 + b \] 3. Solve for \( b \): \[ b = 2 - 3 \] \[ b = -1 \] Now that we have the slope and the y-intercept, we can write the equation of the line: \[ y = 3x - 1 \] Thus, the equation of the line in slope-intercept form is: \[ y = 3x - 1 \]

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The equation of the line is \( y = 3x - 1 \).
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