Final answer:
The equation of the line in standard form that passes through the points (-4,8) and (4,2) is 3x + 4y = 44.
Step-by-step explanation:
To write the equation of a line in standard form, we need to find the slope and the y-intercept. The slope is found using the formula: m = (y2 - y1) / (x2 - x1). Using the points (-4,8) and (4,2), we have m = (2-8) / (4-(-4)) = -6/8 = -3/4. The y-intercept can be found by substituting one of the points into the equation y = mx + b and solving for b. Using the point (-4,8), we have 8 = (-3/4)(-4) + b. Solving for b, we get b = 8 - (3/4)(-4) = 8 + 3 = 11.
Therefore, the equation of the line is y = (-3/4)x + 11. To write it in standard form, we multiply every term by 4 to eliminate the fraction: 4y = -3x + 44. Rearranging the terms, we get 3x + 4y = 44. So the line is in standard form.