Final answer:
To determine the equation of the line in standard form, we start with the point-slope equation, substitute the given point and slope, convert to slope-intercept form, and then rearrange into standard form to obtain -3x + 2y = 14.
Step-by-step explanation:
To write the equation of the line that passes through the point (2,8) with a slope of 3/2 in standard form, we follow these steps:
- Start with the point-slope form of a line: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point through which the line passes.
- Substitute the known values: y - 8 = ¾(x - 2).
- Rearrange the equation to the slope-intercept form y = mx + b, yielding y = ¾ x + 7.
- Convert the slope-intercept form to standard form (Ax + By = C) by clearing the fraction and moving all terms to one side: 2y = 3x + 14, then -3x + 2y = 14.
Therefore, the standard form of the equation is -3x + 2y = 14.