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What is the equation in slope-intercept form of a line that is perpendicular to y=+2 and passes through the point (3, 1)?Enter your answer by filling in the boxes.y=x+IBasicy9¹0741085263X^171A20S

What is the equation in slopeintercept form of a line that is perpendicular to y2 and passes through the point 3 1Enter your answer by filling in the boxesyxIBa class=


Answer :

step 1

Remember that

If two lines are perpendicular, then their slopes are negative reciprocal

so

we have the line

[tex]y=\frac{1}{3}x+2[/tex]

The slope is m=1/3

therefore

The slope of the perpendicular line is m=-3

step 2

Find out the equation of the line in slope-intercept form

[tex]y=mx+b[/tex]

we have

m=-3

point (3,1)

substitute and solve for b

[tex]\begin{gathered} 1=-3(3)+b \\ 1=-9+b \\ b=1+9 \\ b=10 \end{gathered}[/tex]

substitute

[tex]y=-3x+10[/tex]

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