Final answer:
To write the equation of a line passing through two given points in standard form, first calculate the slope, then use one of the points to find the y-intercept, and finally rearrange the equation to standard form.
Step-by-step explanation:
To write the equation of a line in standard form, we need to convert it from slope-intercept form (y = mx + b) to standard form (Ax + By = C).
Step 1: Calculate the slope (m) using the formula: m = (y2 - y1) / (x2 - x1). In this case, (5,3) and (0,7) are the given points, so m = (3 - 7) / (5 - 0) = -4/5.
Step 2: Substitute one of the given points and the slope into the slope-intercept form to find b (the y-intercept). Using (5,3), we have 3 = (-4/5)(5) + b, which simplifies to b = 7.
Step 3: Replace m and b into the slope-intercept form to get the equation: y = (-4/5)x + 7.
Step 4: Multiply the equation by 5 to eliminate the fraction: 5y = -4x + 35.
Step 5: Rearrange the equation to standard form by moving all terms to one side: 4x + 5y = 35. Therefore, the equation of the line passing through (5,3) and (0,7) in standard form is 4x + 5y = 35.