Schmidt Wright
03/30/2024 · Middle School

Find the point slope form of a line with Slope: -2 that passes through \( (4,3) \) \( (y-\square)=\square(x-\square) \) Write the line in slope intercept form below: \( y=\square \)

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To find the point-slope form of a line with a slope of -2 that passes through the point (4, 3), we can use the point-slope formula: \[ y - y_1 = m(x - x_1) \] where \( m \) is the slope, and \( (x_1, y_1) \) is the point the line passes through. Here, \( m = -2 \), \( x_1 = 4 \), and \( y_1 = 3 \). Substituting these values into the formula, we get: \[ y - 3 = -2(x - 4) \] So, in point-slope form, the equation is: \[ (y - 3) = -2(x - 4) \] Now, to write the line in slope-intercept form \( y = mx + b \), we can simplify the point-slope form: 1. Distribute the slope on the right side: \[ y - 3 = -2x + 8 \] 2. Add 3 to both sides: \[ y = -2x + 8 + 3 \] \[ y = -2x + 11 \] Thus, the slope-intercept form of the line is: \[ y = -2x + 11 \] To summarize: - Point-slope form: \( (y - 3) = -2(x - 4) \) - Slope-intercept form: \( y = -2x + 11 \)

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Point-slope form: \( (y - 3) = -2(x - 4) \) Slope-intercept form: \( y = -2x + 11 \)
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