Final answer:
To find the equation of the line, we can use the slope-intercept form of a linear equation. Using the two given points, we can find the slope and the y-intercept. Substituting these values into the slope-intercept form equation gives us the equation of the line in fully reduced form.
Step-by-step explanation:
To find the equation of the line that passes through the points (0, -7) and (5, -1), we can use the slope-intercept form of a linear equation, which is given by y = mx + b, where m is the slope and b is the y-intercept.
First, we need to find the slope (m) of the line. The slope is calculated using the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using the given points, the slope (m) is calculated as follows: m = (-1 - (-7))/(5 - 0) = 6/5.
Now that we have the slope, we can substitute it into the slope-intercept form equation along with one of the points to find the y-intercept (b). Using the point (0, -7), we have -7 = (6/5)(0) + b, which simplifies to -7 = b. Therefore, the y-intercept is -7.
Finally, substituting the slope (m = 6/5) and y-intercept (b = -7) into the slope-intercept form equation, the fully reduced equation of the line is y = (6/5)x - 7. Therefore, the correct answer is (A) y = 1/5x - 7.