To write the equation of a line with an x-intercept of 3 and a y-intercept of 2 in standard form, calculate the slope as -2/3, use the slope-intercept form y = mx + b to create the equation y = (-2/3)x + 2, and rearrange to get 2x + 3y = 6 as the final standard form.
To write the equation of a line in standard form with an x-intercept of 3 and a y-intercept of 2, we need to find the slope first using the intercepts.
The slope (m) is the rise over run, which in this case is (0 - 2)/(3 - 0) because the coordinates of the x-intercept and y-intercept are (3,0) and (0,2) respectively.
Simplifying this gives us a slope of -2/3.
The slope-intercept form of a line is y = mx + b, which can be used here by substituting m with -2/3 and b (the y-intercept) with 2: y = (-2/3)x + 2.
To convert this into standard form, which is Ax + By = C where A, B, and C are integers and A is nonnegative, we would multiply everything by 3 (to eliminate the fraction) and move all terms involving variables to one side: 3y = -2x + 6 becomes 2x + 3y = 6.
Hence, the standard form of the line is 2x + 3y = 6.