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

- The slope of a line whose equation is ax + by = c is
, where a is the coefficient of x and b is the coefficient of y
∵ The equation of the given line is 4x + 3y = 9
∵
, 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
∴ 
∵ The slope of the perpendicular line to the given line is 
- That means reciprocal the fraction and change its sign
∴ The slope of the perpendicular line = 
∵ The form of the equation is y = mx + b
- Substitute m by 
∴ y =
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 =
(-2) + b
∴ 3 =
+ b
- Add
to both sides
∴
= b
∴ y =
x + 
The equation that represents the line that is perpendicular to graph of 4x + 3y = 9 and passes through (-2,3) is y =
x + 
Learn more:
You can learn more about the linear equations in brainly.com/question/1284310
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