Final answer:
The correct equation in slope-intercept form is A) y = -1/3x + 4 2/3, representing a line parallel to x + 3y = 7 and passing through (-1,5). In its standard form, the equation is B) x + 3y = 14.
Step-by-step explanation:
To write an equation for a line that is parallel to another and passes through a given point, we must first understand the concepts of slope and y-intercept. The given equation, x + 3y = 7, can be rewritten in slope-intercept form (y = mx + b) to determine its slope. Reordering x + 3y = 7 gives us 3y = -x + 7, which simplifies to y = -1/3x + 7/3. This shows that the slope (m) of the line is -1/3.
Since parallel lines have the same slope, the line passing through the point (-1,5) will also have a slope of -1/3. To find the y-intercept (b), we use the coordinates of the given point in the slope-intercept equation y = mx + b: 5 = (-1/3)(-1) + b, which simplifies to 5 = 1/3 + b. Solving for b gives b = 5 - 1/3, which is 14/3 or 4 and 2/3.
The equation in slope-intercept form is therefore y = -1/3x + 14/3, which can be written as A) y = -1/3x + 4 2/3. To convert this equation to the standard form, A x + By = C, we multiply through by 3 to get rid of the fraction: 3y = -x + 14. Reordering to get the x and y terms on the left side gives us B) x + 3y = 14, which is the correct equation in standard form.