The equation in slope-intercept form, of the line that passes through (6, -5) and is parallel to the line given is: D. [tex]\mathbf{y = -\frac{3}{2} x + 4}[/tex]
Recall:
- Slope of two lines that are parallel to each other will always be the same value.
From the graph shown, the slope (m) of the line is [tex]-\frac{3}{2}[/tex].
Thus, the line that passes through (6, -5) and is parallel to the line in the graph will have the same slope of [tex]-\frac{3}{2}[/tex].
Write the equation in point-slope form by substituting (a, b) = (6, -5) and m = -3/2 into y - b = m(x - a).
[tex]y - (-5) = -\frac{3}{2} (x - 6)\\\\y +5 = -\frac{3}{2} (x - 6)[/tex]
Rewrite in point-slope form as y = mx + b
[tex]y +5 = -\frac{3}{2} (x - 6)\\\\y + 5 = -\frac{3}{2} x + 9\\\\y = -\frac{3}{2} x + 9 - 5\\\\\mathbf{y = -\frac{3}{2} x + 4}[/tex]
- Therefore, the equation in slope-intercept form, of the line that passes through (6, -5) and is parallel to the line given is: D. [tex]\mathbf{y = -\frac{3}{2} x + 4}[/tex]
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