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(A) Find the slope of the line that passes through the given points. (B) Find the poind-slope lorm of the equation of the line. (C) Find the slope-intercept form of the equation of the line (D) Find the standard lorm of the equation of the Ine. \( (-5,4) \) and \( (1,4) \) (A) Select the corect choice below and, if necessary, fill in the answer box to complete your choice. A. \( m=\square \) (Type an integer or a simplified fraction.) B. The slope is not defined.

Ask by Long Potter. in the United States
Jan 21,2025

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**A. \( m = 0 \)**

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The Deep Dive

To find the slope of a line passing through the points (-5, 4) and (1, 4), we notice that both points have the same y-coordinate. This signifies that the line is horizontal. Therefore, the slope is calculated as \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 4}{1 - (-5)} = \frac{0}{6} = 0 \]. A smooth slope of zero means you can have a leisurely stroll along it without any uphill battles! Now, for the point-slope form of the equation, since we know the slope \( m = 0 \), we can use one of the points. Using the point (-5, 4), the point-slope form is given as \( y - y_1 = m(x - x_1) \), which gives us \( y - 4 = 0(x + 5) \) or simply \( y = 4 \). No hiccups here; this horizontal line is steady as she goes!

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