Write a linear equation that is perpendicular to y=-4x-6 and passes through the point (4,10).

The equation we look for must have a slope that is the inverse reciprocal of -4. The inverse reciprocal always leads to -1 when multiplied by the given slope.

Let's see: -4(1/4) = -1.

Yep. The slope of the equation we need to find is 1/4.

Use the point-slope formula to find your equation.

Point-slope: y - y_1 = m(x - x_1), where m is the slope, y_1 is the y-coordinate of the given point and x is the x-coordinate of the given point.

We now plug, chug and isolate y.

Ready?

y - 10 = (1/4)(x - 4)

y - 10 = (1/4)x -1

y = (1/4)x - 1 + 10

Your equation is y = (1/4)x + 9.

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