Question

Identify the equation in slope-intercept form for the line containing the point (2,4) and perpendicular to y=1/2x+1/2.

Answer 1

y = − 2 x

Explanation:

Y + 2 = − 2 ⋅ ( − 1 ) Write in y = m x + b form.

The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.

m in perpendicular = − 1 2

(1,-2),y=(1)/(2)x+4

I hope I helped!

Answer 2

y = -2x + 8

Explanation:

For this problem we need to consider that the equation of a line perpendicular to another line will have a "negative reciprocal" slope so that when they cross, it forms a 90-degree angle, hence perpendicular. Additionally, we will need to use the point-slope form and re-write it into the slope-intercept form to incorporate (2,4) into our equation. With these things in mind, let's do that.

y = (1/2)x + (1/2)

We want a "negative reciprocal" so:

y = -2x + (1/2)

Since -2 is the "negative reciprocal" of 1/2.

And now we want to use the point-slope form to incorporate (2,4)

y - y0 = -2 ( x - x0 )

Where, y0 = 4 and x0 = 2.

y - y0 = -2 ( x - x0 )

y - 4 = -2 ( x - 2 )

y - 4 = -2x + 4

y = -2x + 8

So, the equation that is perpendicular to y = (1/2)x + (1/2) and includes the point (2,4) is y = -2x + 8.

Cheers.