Find an equation of the line in the form ax+by=C. The line with Y-intercept is -3 and perpendicular to x+6y=19.?

Since the required line has a y-intercept of - 3, then its rough equation will be…

y = mx - 3

in the slope-intercept form.

Next, it becomes necessary to find the slope of the required line.

It is specified that the required line is perpendicular to the line having the

equation of…

x + 6y = 19

This is converted to the slope-intercept form…

x + 6y = 19

x - x + 6y = - x + 19

6y = - x + 19

6y/6 = - x/6 + 19/6

y = - x/6 + 19/6

The given equation is now in the slope-intercept form where…

m = - 1/6

b = 19/6

A perpendicular line has a slope that is the negative reciprocal of the first line.

In other words, if m1 is the slope of the first line and m2 is the slope of the

perpendicular line, then…

m2 = - 1/m1

Since, in this case…

m1 = - 1/6

then

m2 = - 1/(-1/6)

m2 = 6

Therefore, the slope-intercept form of the required line is…

y = 6x - 3

Then there's a little rearranging to get it into the standard form of ax + by = c.

y = 6x - 3

y = 6x - 3

- 6x + y = 6x - 6x - 3

- 6x + y = - 3 ANSWER

the slopes of perpendicular lines are negative reciprocals

find first the slope of the line x + 6y = 19

x + 6y = 19

6y = -x + 19

divide both sides of the equation by 6

6y/6 = (-x + 19)/6

y = -1/6x + 19/6

the slope m is -1/6, the negative reciprocal of -1/6 is 6, now find the equation of the line that has a y-intercept of -3

from y = mx + b, m = 6, b is -3

plug in the values of m and b

y = mx + b

y = 6x - 3

subtract 6x from both sides

y - 6x = 6x - 6x - 3

y - 6x = -3

x+6y=19

6y= -x + 19

y = (-x/6) + 19/6

Equation = y = (-x/6) - 3

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