is the slope and b is the y-intercept.
a) The y-intercept of a line defined by the equation y - ax - b = 0 is the coordinate (0, b). If we look at the equation y-6x-10=0, we can see that in this case, b is -10, so the y-intercept is (0, -10). But in the given equation, the sign before 10 is negative, which means the y value is subtracted by 10. This makes the y-intercept (0, 10).
b) To find the slope of the line -1x-7y=-12, the equation needs to be rewritten in the form y = ax + b, where a is the slope. By rearranging the equation to this form, we get y = x/7 - 12/7. Therefore, the slope of this line is 1/7.
Since the two lines need to be parallel, they will have the same slope. Using the y-intercept from part a) and the slope from part b), we can plug these values back into the equation y = mx + b to get the equation of the line: y = 1/7*x + 10.
So, the equation of the line that has the same y-intercept as the line y-6x-10=0 and is parallel to the line -1x-7y=-12 is y = 1/7*x + 10.