Answer:
[tex]y = 1[/tex]
[tex]y-5=3(x+2)[/tex]
Step-by-step explanation:
The line [tex]y = -2[/tex] is a horizontal line.
Therefore, a line that is parallel to the given line and passes through point (-1, 1) is another horizontal line with the y-value of the point.
Therefore, the line is [tex]y = 1[/tex]
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Slope-intercept form of a linear equation:
[tex]y=mx+b[/tex]
where:
- m is the slope
- b is the y-intercept
Given linear equation:
[tex]y=-\dfrac{1}{3}x+2[/tex]
Therefore, the slope of this equation is -1/3.
If two lines are perpendicular to each other, the product of their slopes will be -1. Therefore, the slope (m) of the line perpendicular to the given line is:
[tex]\implies m \cdot -\dfrac{1}{3}=-1[/tex]
[tex]\implies m=3[/tex]
Use the point-slope form of a linear equation, with the found slope and the point (-2, 5) to create the equation:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-5=3(x-(-2))[/tex]
[tex]\implies y-5=3(x+2)[/tex]
