Question

Which equation represents the line that is perpendicular to graph of 4x+3y=9 and passes through (-2,3)

Answer 1

4y = 3x + 18

Step-by-step explanation:

NOTE THAT A line that is perpendicular to another has a negative inverse of the slope of the other line. The products of their slopes, that is, is always -1

Therefore we can begin by finding the slope of this line defined by the function 4x+3y=9

3y = -4x + 9

y = -4/3 x + 9/3

y = -4/3 x + 3

The slope of the  perpendicular line is, therefore;

¾  - this is the negative inverse of -4/3

Now that we know the slope, we need to find the y-intercept. This is where x = 0 and the line meets the y-axis;

i.e (0, y)

The other given point, where the line crosses  is (-2, 3). Remember that to get the gradient we use the formula;

Gradient = Δ y / Δ x

¾ = (3 – y) / (-2 – 0)

¾ = (3 –y) / -2  

¾ * -2 = 3 – y

-3/2 = 3 – y

-3/2 – 3 = -y

9/2 = y           ←– This is the y-intercept

Remember the function of a straight line is given;

y = mx + c (m being slope and c being y-intercept)

y = 3/4 x + 9/2

4y = 3x + 18

Learn More:

brainly.com/question/2783474

brainly.com/question/14148974

#LearnWithBrainly

Answer 2

The equation that represents the line  that is perpendicular to graph of 4x + 3y = 9 and passes through (-2,3) is y = $\frac{3}{4}$ x + $\frac{9}{2}$

Step-by-step explanation:

Let us revise some rules

• The product of the slopes of the perpendicular line is -1, that means if the slope of one line is m, then the slope of the other is $\frac{-1}{m}$
• The slope of a line whose equation is ax + by = c is $m=\frac{-a}{b}$ , where a is the coefficient of x and b is the coefficient of y

∵ The equation of the given line is 4x + 3y = 9

∵ $m=\frac{-a}{b}$ , where a is the coefficient of x and b

   is the coefficient of y

∵ The coefficient of x = 4 and the coefficient of y = 3

∴ a = 4 and b = 3

∴ $m=\frac{-4}{3}$

∵ The slope of the perpendicular line to the given line is $\frac{-1}{m}$

- That means reciprocal the fraction and change its sign

∴ The slope of the perpendicular line = $\frac{3}{4}$

∵ The form of the equation is y = mx + b

- Substitute m by $\frac{3}{4}$

∴ y = $\frac{3}{4}$ x + b

- To find b substitute x and y in the equation by the coordinates

 of a point on the line

∵ The perpendicular line passes through point (-2 , 3)

∴ x = -2 and y = 3

∵ 3 = $\frac{3}{4}$ (-2) + b

∴ 3 = $\frac{-3}{2}$ + b

- Add $\frac{3}{2}$ to both sides

∴ $\frac{9}{2}$ = b

∴ y = $\frac{3}{4}$ x + $\frac{9}{2}$

The equation that represents the line  that is perpendicular to graph of 4x + 3y = 9 and passes through (-2,3) is y = $\frac{3}{4}$ x + $\frac{9}{2}$

Learn more:

You can learn more about the linear equations in brainly.com/question/1284310

#LearnwithBrainly