Find the equation of the line that passes through the points (2/3, -5/4)and (-3, -5/6). Write the answer in slope-intercept form and standard form with integer coefficients.

Thank you.

(y+5/4)/(x-2/3) = (-5/6 + 5/4)/(-3 - 2/3)

3(4y+5) / 4(3x-2) = 5/12 / -11/3 = -5/44

3(4y+5) = -5/44 * 4(3x-2)
12y + 15 = -5/11 * (3x-2)
12y = -15/11 x + 10/11 - 15
12y = -15/11 x - 155/11
y = -5/44 x - 155/132

clear fractions and rearrange for standard form

What is 475.189 rounded to the nearest hundredth?

To find the equation of the line, we will use the formula for the equation of a line:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line, and m is the slope of the line.

First, let's find the slope of the line using the two given points (2/3, -5/4) and (-3, -5/6).

The slope (m) is given by the formula:

m = (y2 - y1) / (x2 - x1)

Let's substitute the given values into the formula:

m = (-5/6 - (-5/4)) / (-3 - 2/3)

Let's simplify:

m = (-5/6 + 5/4) / (-3 - 2/3)
= (-5/6 + 15/12) / (-9/3 - 2/3)
= (-10/12 + 15/12) / (-11/3)
= 5/12 / (-11/3)
= 5/12 * (-3/11)
= -15/132
= -5/44

Now that we have the slope (m), we can pick any of the given points to substitute into the formula. Let's use (2/3, -5/4). So we have:

y - (-5/4) = (-5/44)(x - 2/3)

Simplifying:

y + 5/4 = (-5/44)(x - 2/3)

To get the equation in slope-intercept form (y = mx + b), we need to isolate y. Let's continue simplifying:

y = (-5/44)(x - 2/3) - 5/4
= (-5/44)x + 10/132 + (-5/4)
= (-5/44)x + 10/132 - (5/4)(33/33)
= (-5/44)x + 10/132 - 165/132
= (-5/44)x - 155/132

Now let's simplify the equation to standard form (Ax + By = C) with integer coefficients:

Multiply through by 44 to clear the fraction:

44y = -5x - (44)(155)

Rearranging the terms:

5x + 44y = -6820

So, the equation of the line in slope-intercept form is y = (-5/44)x - 155/132, and in standard form with integer coefficients is 5x + 44y = -6820.