The equation of the line in slope-intercept form, that passes through (-1, 2) and is parallel to the line, y = -3x is: [tex]\mathbf{y = -3x - 1}[/tex] (none of the options are correct)
Recall:
Slope-intercept form of a line's equation is: [tex]y = mx + b[/tex]
slope = m
y-intercept = b
Point-slope form is: y - b = m(x - a)
Lines that are parallel to each other have the same slope.
Given the line equation: y = -3x
The slope is -3.
The line that is parallel to y = -3x will also have a slope of -3.
If the line passes through (-1, 2), to write the equation of the line, substitute (a, b) = (-1, 2) and m = -3 into y - b = m(x - a).
Thus:
[tex]y - 2 = -3(x - (-1))\\\\y - 2 = -3(x + 1)\\\\y - 2 = -3x - 3\\\\y = -3x - 3 + 2\\\\\mathbf{y = -3x - 1}[/tex]
The equation of the line in slope-intercept form, that passes through (-1, 2) and is parallel to the line, y = -3x is: [tex]\mathbf{y = -3x - 1}[/tex] (none of the options are correct)
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