Final answer:
To write the equation in standard form, find the slope using the two given points and then use the point-slope form to obtain the equation. Rearrange the equation to get the coefficients as integers in descending order.
Step-by-step explanation:
To write an equation in standard form, we need to rearrange it so that the coefficients (the numbers multiplied by the variables) are all integers, and the variables are in descending order.
Given that the x-intercept is (2,0) and the y-intercept is (0,-6), we can use these points to find the equation of the line.
The slope of the line can be found using the formula m = (y2 - y1)/(x2 - x1). Substituting the values, we get m = (-6 - 0)/(0 - 2) = -6/(-2) = 3.
Now, we can use the point-slope form of the equation, y - y1 = m(x - x1), and substitute the values of (0,-6) and m = 3 to get y - (-6) = 3(x - 0), which simplifies to y + 6 = 3x. Rearranging the equation to standard form, we get 3x - y = -6.