Question

Find the equation of the line which is perpendicular to the line.

(a) with equcation y=5x-4 and passes through (0,7)

Answer 1

`y = - (1)/(5) x + 7`

Explanation:

Slope -intercept form:

y= mx +c, where m is the slope and c is the y- intercept.

Since the given equation is already in the slope-intercept form, we can identify its slope by looking at the coefficient of x.

Slope of given line= 5

The product of the gradients of two perpendicular lines is -1.

m(5)= -1

`m = - (1)/(5)`

Substitute the value of m into the equation:

`y = - (1)/(5) x + c`

Substitute a pair of coordinates to find the value of c.

when x= 0, y= 7,

`7 = - (1)/(5) (0) + c`

c= 7

Thus, the equation of the line is y= -⅕x +7.