To find the standard form of the equation of a line given a point and a slope, we can start with the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
Given the point (1, 2) and the slope m = 7, we first use this point to find b. Plugging the values into the slope-intercept equation:
2 = 7(1) + b
Solving for b:
2 = 7 + b
b = 2 - 7
b = -5
Now, substituting back to the slope-intercept form, we have:
y = 7x - 5
Next, to convert this to standard form, we rearrange it to the form Ax + By = C. Starting from y = 7x – 5, we can rearrange it:
-7x + y = -5
To express it in standard form where A is a positive integer, we multiply the entire equation by -1:
7x - y = 5
Thus, the standard form of the equation of the line through the point (1, 2) with a slope of 7 is:
7x - y = 5