The equation for line v can be written as y = –1 5 x + 9 .

Question

The equation for line v can be written as y = –1 5 x + 9 .Line w is perpendicular to line v and passes through (2, 6) .What is the equation of line w? Write the equation in slope-intercept form. Write the numbers in the equation as proper fractions

Answer 1

The slope-intercept form is the general equation for a straight line or y = mx + b.

m is the gradient of the line, and b is the y intercept (where the line crosses the y axis).

This equation form is very important in helping you draw lines, and figure out their equations.

The additional key piece of information you need is that if two lines are perpendicular, the product of their gradients is -1. In maths-speak m1.m2 = -1

The problem gives us the line V, with equation y = -15x + 9.

For this line (by comparing with y = mx + b), the gradient is -15. A negative gradient goes down and to the right. 15 is a steep gradient, so for one unit across, the line goes down 15 units.

The y intercept is 9, so the line passes through the point (0,9).

You could now draw the line on your graph paper, which you might find helpful to see what it looks like. However, if the question doesn't ask you to draw it, then you don't need to.

So, now, let's figure out the equation of the perpendicular line W.

We start with the general equation y = mx + b

And we know that m1.m2 = -1 and m1 (gradient of first line V) is -15

hence -15 x m2 = -1

and m2 = 1/15

because it's positive, it goes up and to the right. because it's a fraction, the line is very shallow, going up only 1 unit when you go 15 units across.

Now, the equation becomes y = (1/15)x + b

We still don't know b, but we do know that this line passes through the point (2,6). So we can substitute these values to find b.

6 = (1/15)(2) + b

=>6 = (2/15) + b

=> b = 6 - (2/15) = 88/15 [or 5 13/15 if you prefer]

This means W passes through both (2,6) and (0, 5 13/15)

And it means the equation for W is y = (1/15)x + 88/15 or 15y = x + 88.

Normally, I would use 15y form as it's neater and gets rid of the fractions. However, as the question specifically asks for the slope intercept form and proper fractions I would write y = 1/15 x + 5 13/15.