Final answer:
a. The equation for the line in point-slope form is y + 9 = 4(x - 9), with a slope of 4.
b. The equation can be rewritten in standard form as 4x - y = 45.
Step-by-step explanation:
a. To write the equation for the line in point-slope form, we need to determine the slope (m) and one point on the line (x1, y1).
The slope can be calculated using the formula m = (y2 - y1) / (x2 - x1).
Taking the points (9, -9) and (10, -5), we can substitute the values into the formula to get m = (-5 - (-9)) / (10 - 9) = 4 / 1 = 4.
Now we can use the formula y - y1 = m(x - x1) with the point (9, -9) to get y - (-9) = 4(x - 9). Simplifying, we have y + 9 = 4x - 36.
b. To rewrite the equation in standard form, we need to bring the equation to the form Ax + By = C, where A, B, and C are integers.
Starting from the point-slope form, we can expand and simplify the equation to get y + 9 = 4x - 36 becomes y = 4x - 45.
To make all the coefficients integers, we can multiply the equation by 5 to get 5y = 20x - 225, rearrange the terms as -20x + 5y = -225, and divide every term by -5 to get the standard form 4x - y = 45.