To write an equation for a line that is parallel to the line y = 9x - 2 and passes through the point (7. -3), we need to first understand that parallel lines have the same slope. This means our new line will also have a slope (m) of 9.
The general equation for a line in slope-intercept form is y = mx + b, where m is the slope, b is the y-intercept, and x and y are the coordinates. For the given line, the y-intercept (b) is what we don't know yet and need to solve for.
We are given a point through which the line we seek passes, (x, y) = (7, -3). Plug in these values along with m = 9 into the equation y = mx + b.
That gives us -3 = 9*7 + b.
Next, we solve this equation for b.
Subtract 9*7 from both sides of the equation to get b alone on one side. This yields
b = -3 - 9*7
b = -3 - 63
b = -66
So, the y-intercept (b) of our line is -66. Insert m = 9 and b = -66 in the equation y = mx + b to get the equation for the line:
y = 9x - 66
Therefore, the equation of the line that passes through the point (7, -3) and is parallel to the line y = 9x - 2 is y = 9x - 66.