Find an equation of the line in the form axplusbyequalsc whose x-intercept is 9 and y-intercept is 3, where a, b, and c are integers with no factor common to all three, and agreater than or equals0.

x intercepts and y intercepts will give us 2 points lying on that line. Then using those points, we can evaluate a, b, and c.

The equation of specified line is:  

Equation of specified line.

The x intercept, since lying on x axis, has its y ordinate 0, thus its coordinate being (9, 0)

The y intercept, since lying on y axis, has its x abscissa 0, thus its coordinate being (0, 3)

Since both point lies on the given line, thus both will satisfy the equation of that line:

and

Thus, from both equation:

Thus, equation of line is given by:

Thus, equation of specified line is

Learn more about equation of straight line here:

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Standard Form: Ax + By = C  

x-intercept = 9:   A(9) + B(0) = C   ⇒ 9A = C

y-intercept = 3:    A(0)  + B(3) = C  ⇒ 3B = C

Using substitution, 9A = 3B   ⇒  3A = B

Ax + By = C  ⇒  Ax + (3A)y = C    

3x + 9y = 27   →  x + 3y = 9

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1