Final answer:
The standard form of the equation of the line that passes through (-5,0) and (0,-9) is 9x + 5y = -45, which is option b.
Step-by-step explanation:
To determine the standard form of the equation of the line that passes through the points (-5,0) and (0,-9), we first need to calculate the slope of the line using the formula m = (y2 - y1) / (x2 - x1). Plugging in our points, we get m = (-9 - 0) / (0 - (-5)) = -9 / 5.
Now that we have the slope, we can use point-slope form to write the equation of the line. Point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Using point (-5,0), the equation becomes y - 0 = (-9/5)(x - (-5)).
Simplifying, we get y = (-9/5)x - 9. To transform this into standard form, which is Ax + By = C, we multiply everything by 5 to eliminate the fraction: 5y = -9x - 45. Rearranging, we have 9x + 5y = -45, so the correct standard form of the line is option b. 9x + 5y = -45.