Final answer:
The equation of a line with a slope of 2 passing through (7,9) in point-slope form is 'y - 9 = 2(x - 7)', which can be rearranged to slope-intercept form 'y = 2x - 5' and standard form '2x - y = 5'.
Step-by-step explanation:
To write the equation for a line with a slope of 2 that passes through the point (7,9), we start with the point-slope form of a line's equation:
y - y1 = m(x - x1).
Here, (x1, y1) is the point the line passes through, and m is the slope of the line. In this case, (x1, y1) is (7,9) and m = 2. Substituting these values, we get:
y - 9 = 2(x - 7).
Now, to convert this into slope-intercept form (y = mx + b), we expand and rearrange the equation:
y - 9 = 2x - 14
y = 2x - 5.
This is our slope-intercept form where the slope is 2 and the y-intercept is -5.
Finally, to convert to standard form (Ax + By = C), we move all terms to one side of the equation:
-2x + y = -5.
However, standard form typically requires A to be positive, so we multiply through by -1:
2x - y = 5.