Question

Nrite an equation in slope-intercept form of the line that satisfie Through (9,2); perpendicular to 3x-y=9

Answer 1

Answer:
`y=(-1)/(3) x+5`

Explanation:

To find our equation first, we have to turn 3x-y=9 into a slope-intercept form:
`y=mx+b`

`3x-y=9\\-3x=-3x\\-y=-3x+9` subtract -3x on both sides

`(-y)/(-1) =(-3x)/(-1) (+9)/(-1)` divide -y, -3x, and 9 by -1

`y=3x-9`

Now we have this line in slope intercept form we can find our equation by using the point (9,2), point-slope formula
`y-y_(1) =m(x-x_(1) )` , and the opposite reciprocal of 3x (slope) which is
`(-1)/(3)x` for the slope of the perpendicular line

`y-2 =(-1)/(3) x(x-9 )` distribute
`(-1)/(3)x`

`y-2 =(-1)/(3) x+3\\+2=+2\\y=(-1)/(3) x+5`add 2 on both sides

`y=(-1)/(3) x+5`

So now we have the perpendicular line in slope intercept form we can start to plot points to make our line.

We start at our y-intercept (0,5) then go down 1 unit and to the right 3 units until we get to (9,2) to draw our perpendicular line

(0,5)

(3,4)

(6,3)

(9,2)

Now we can draw our perpendicular line
`y=(-1)/(3) x+5`

Answer 2

Explanation:

To find the equation of a line that is perpendicular to the given line and passes through the point (9, 2), we need to follow these steps:

Find the slope of the given line.

Determine the negative reciprocal of the slope (perpendicular slope).

Use the point-slope form of a linear equation to write the equation.

Given line: 3x - y = 9

Find the slope of the given line:

The equation is in the form y = mx + b, where "m" is the slope. Rearrange the equation to solve for y:

y = 3x - 9

So, the slope of the given line is 3.

Determine the negative reciprocal of the slope:

The negative reciprocal of 3 is -1/3.

Use the point-slope form of a linear equation (y - y₁ = m(x - x₁)):

Point: (9, 2)

Slope: -1/3

Now plug in the values to get the equation:

y - 2 = -1/3(x - 9)

Simplify the equation:

y - 2 = -1/3x + 3

Add 2 to both sides:

y = -1/3x + 5

So, the equation of the line that is perpendicular to 3x - y = 9 and passes through the point (9, 2) is y = -1/3x + 5.