Final answer:
The equation of the line in standard form that goes through the points (-5, 2) and (-4, 3) is x - y = -7, calculated by first finding the slope using the given points, then using one of the points to find the y-intercept, and finally rearranging the equation into standard form.
Step-by-step explanation:
To write the equation of a line in standard form (Ax + By = C) that goes through the points (-5, 2) and (-4, 3), we need to first calculate the slope of the line using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points. Substituting the given points into the formula, we get m = (3 - 2) / (-4 + 5) = 1. The slope-intercept form of the line is y = mx + b. Substituting the slope and one of the given points (-5, 2) into this form to solve for b, we get 2 = 1(-5) + b, leading to b = 7. Therefore, the equation in slope-intercept form is y = 1x + 7. To convert this to standard form, we rewrite it as x - y = -7. However, standard form typically requires the coefficients of x and y to be integers, so we don't have to change anything further.