Please help!!!!
Write three equations whose graphs are the same line as the equation -9x + 5y = -4.

9514 1404 393

Answer:

Step-by-step explanation:

The intercepts are ...

  x-intercept = -4/-9 = 4/9

  y-intercept = -4/5

Knowing these intercepts means we can put the equation in intercept form.

  x/(4/9) -y/(4/5) = 1

The fractional intercepts make graphing somewhat difficult. However, we observe that the sum of the x- and y-coefficients is equal to the constant:

  -9 +5 = -4

This means the point (x, y) = (1, 1) is on the graph. Knowing a point, we can write several equations using that point.

We like a positive leading coefficient (as for standard or general form), so we can multiply the given equation by -1.

  9x -5y = 4 . . . . . standard form equation

Adding -4, so f(x,y) = 0, puts this in general form.

  9x -5y -4 = 0

We can eliminate the constant by translating a line from the origin to the point we know:

  9(x -1) -5(y -1) = 0

This can be rearranged to the traditional point-slope form ...

  y -1 = 9/5(x -1)

Yet another equation can be written that tells you the slope is the same everywhere:

  (y -1)/(x -1) = 9/5

These are only a few of the many possible forms of a linear equation.

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