The equation that represents the line that is perpendicular to graph of 4x + 3y = 9 and passes through (-2,3) is y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
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 [tex]\frac{-1}{m}[/tex]
- The slope of a line whose equation is ax + by = c is [tex]m=\frac{-a}{b}[/tex] , where a is the coefficient of x and b is the coefficient of y
∵ The equation of the given line is 4x + 3y = 9
∵ [tex]m=\frac{-a}{b}[/tex] , 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
∴ [tex]m=\frac{-4}{3}[/tex]
∵ The slope of the perpendicular line to the given line is [tex]\frac{-1}{m}[/tex]
- That means reciprocal the fraction and change its sign
∴ The slope of the perpendicular line = [tex]\frac{3}{4}[/tex]
∵ The form of the equation is y = mx + b
- Substitute m by [tex]\frac{3}{4}[/tex]
∴ y = [tex]\frac{3}{4}[/tex] 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 = [tex]\frac{3}{4}[/tex] (-2) + b
∴ 3 = [tex]\frac{-3}{2}[/tex] + b
- Add [tex]\frac{3}{2}[/tex] to both sides
∴ [tex]\frac{9}{2}[/tex] = b
∴ y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
The equation that represents the line that is perpendicular to graph of 4x + 3y = 9 and passes through (-2,3) is y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{9}{2}[/tex]
Learn more:
You can learn more about the linear equations in brainly.com/question/1284310
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