Respuesta :
The area of a triangle bounded by the y-axis is 8.49 square units
Solution:
Given that f(x) = [tex]6 - \frac{5}{7}x[/tex]
[tex]\text { Let } y=6-\frac{5}{7} x[/tex]
[tex]y = \frac{-5}{7}x + 6[/tex]
On comparing the above equation with slope intercept form.i.e
y = mx + c
where "m" is the slope and "c" is the y-intercept
So slope = [tex]\frac{-5}{7}[/tex]
We know product of slopes of perpendicular line and given line is always -1
Slope of perpendicular line is given as:
[tex]= \frac{7}{5}[/tex]
Equation of perpendicular line passing through origin (0, 0) is:
y = mx + c
[tex]y = \frac{7}{5}x + 0\\\\y = \frac{7}{5}x[/tex]
Intersecting point between the lines is:
[tex]\frac{7}{5}x = 6 - \frac{5}{7}x\\\\\frac{7}{5}x + \frac{5}{7}x = 6[/tex]
[tex]\frac{74x}{35} = 6\\\\x = 2.83[/tex]
We know that [tex]y = \frac{7}{5}x[/tex]
[tex]y = \frac{7 \times 2.83}{5}\\\\y = 3.962[/tex]
Point is (2.83, 3.962)
y intercept of line is [tex]y = 6 - \frac{5}{7}x\\[/tex]
Put x = 0
Therefore y = 6
So the triangle is bounded by the points (0, 0) and (0, 6) and (2.83, 3.962)
[tex]\text { Area of triangle }=\frac{1}{2} \times 6 \times 2.83=8.49[/tex]
Thus area of triangle is 8.49 square units
