Find an equation in the slope - intercept form to the line that passes through (-5,-7) and is parallel to x +9y = -37

parallel to x+9y=-37 or y=-1/9 x + ...

so the slope is -1/9 to be parallel.

y= -x/9 + b
put in (-5,-7) and you have b, and the line equation is solved.

I hoping all of the steps would be written out as it has been awhile since I have had a math class.

a. find the slope of the line x+9y=-37, you should get -1/9 as above.

b. now write the standard equation with that slope
y=-x/9 + b
put the point in, and solve for b.

To find an equation in slope-intercept form for a line parallel to a given line, we need to determine the slope of the given line first.

The equation x + 9y = -37 is in standard form. We can rewrite it in slope-intercept form (y = mx + b) to determine the slope (m).

Step 1: Subtract x from both sides.
9y = -x - 37

Step 2: Divide every term by 9 to solve for y.
y = -x/9 - 37/9

Now that we have the slope of the given line, which is -1/9, we can use this slope to find the equation of the line parallel to it.

Parallel lines have the same slope, so the line we are looking for also has a slope of -1/9.

Using the point-slope form (y - y1 = m(x - x1)), where (-5, -7) is a given point on the line, and -1/9 is the slope, we can substitute the values into the equation.

y - (-7) = (-1/9)(x - (-5))
y + 7 = (-1/9)(x + 5)

Now, we can simplify and rewrite the equation in slope-intercept form.

y + 7 = (-1/9)x - 5/9

Subtract 7 from both sides:

y = (-1/9)x - 5/9 - 7
y = (-1/9)x - 5/9 - 63/9
y = (-1/9)x - 68/9

Therefore, the equation in slope-intercept form for the line passing through (-5, -7) and parallel to the line x + 9y = -37 is y = (-1/9)x - 68/9.