Final answer:
The standard form of the line through the point (1,2) with a slope of 7 is 7x - y = 5. This is obtained by inserting the point and the slope into the point-slope form equation and then rearranging to standard form.
Step-by-step explanation:
To write the equation of a line in standard form given a point and a slope, you can use the point-slope form,
y - y1 = m(x - x1),
where m is the slope and (x1, y1) is the point the line passes through.
In this case, the point is (1,2) and the slope is 7.
You would plug these into the point-slope form to get y - 2 = 7(x - 1).
Next, you'll want to rearrange this into standard form, which is Ax + By = C.
After distributing and moving terms around, you should get 7x - y = 5.
Remember, standard form generally requires A, B, and C to be integers, and A should be positive.
- Start with point-slope form: y - 2 = 7(x - 1)
- Distribute the 7: y - 2 = 7x - 7
- Add 2 to both sides: y = 7x - 5
- Subtract y from both sides: -y = -7x + 5
- Multiply by -1 to get positive A: 7x - y = 5
The standard form of the line through (1,2) with a slope of 7 is 7x - y = 5.