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Write the equation of the line that is perpendicular to the graph of y = x + 6 and whose y-intercept is (0, -2)

Sagot :

Perpendicular lines are straight lines that intersect at right angles. The slope of the line with equation y = 1/x + 6 is 1.

If you multiply the slopes of two perpendicular lines, we get -1.

[tex]\frac{1}{2}\times(-2)=-1[/tex]

Thus, the line perpendicular to y = 1/2x + 6 has the slope -2

Now use the intercept-slope form to find the equation.

[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)=-2(x-0) \\ y+2=-2x \\ y+2-2=-2x-2 \\ y=-2x-2 \end{gathered}[/tex]

Therefore, the line y = -2x-2 is perpendicular to the line y=1/2x+6 and passes through the y-intercept (0,2)

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