Final answer:
The equation in standard form for the line passing through the points (4,5) and (6,11) is found by first calculating the slope, then using the point-slope equation, and finally rearranging to get 3x - y = 7.
Step-by-step explanation:
To write an equation in standard form for the line passing through the points (4,5) and (6,11), we first need to calculate the slope of the line. The slope (m) can be determined using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two given points. Using the points (4,5) and (6,11), we find the slope to be:
m = (11 - 5) / (6 - 4) = 6 / 2 = 3.
Once we have the slope, we can use the point-slope form of the line equation, y - y1 = m(x - x1), and insert one of the points and the slope. For point (4,5) and slope 3, that would be:
y - 5 = 3(x - 4)
Expanding this equation:
y - 5 = 3x - 12
Move all terms to one side to get the standard form Ax + By = C:
-3x + y = -7
To get positive coefficients for A, we can multiply through by -1:
3x - y = 7
This is the standard form of the equation of the line.