Question
What is the gradient of a line parallel to the line whose equation -2x + y = -7 is:
Hint:
The slope/ gradient of a line is the measure of steepness of a line. It is understood that the slope of all parallel lines in the xy plane are equal. So first, we find the slope from the given equation of a line by using the slope intercept form of a line which is y = mx + c, , where m is slope and c is the y intercept. This gradient will be equal to the gradient of any line parallel to it.
The correct answer is: the gradient of a line parallel to the line whose equation -2x + y = -7 is m = 2.
Step by step solution:
The given equation of the line is
-2x + y = -7
We convert this equation in the slope intercept form, which is
y = mx + c
Where m is the slope of the line and c is the y-intercept.
We rewrite the equation -2x + y - 7, as below
y = 2x - 7
Comparing with y = mx + c, we get that m = 2
Thus, the gradient of line -2x + y = 7 is m = 2.
We know that the gradient of any two parallel lines in the xy plane is always equal.
Hence, the gradient of a line parallel to the line whose equation -2x + y = -7 is m = 2.
We convert this equation in the slope intercept form, which is
Where m is the slope of the line and c is the y-intercept.
We rewrite the equation -2x + y - 7, as below
Comparing with y = mx + c, we get that m = 2
Thus, the gradient of line -2x + y = 7 is m = 2.
We know that the gradient of any two parallel lines in the xy plane is always equal.
Hence, the gradient of a line parallel to the line whose equation -2x + y = -7 is m = 2.
We can find the slope and y-intercept directly from the general form of the equation too; slope =
and y-intercept = 
, where the general form of equation of a line is ax + by + c = 0. Using this method, be careful to check that the equation is in general form before applying the formula. Here, we have, a = -2, b = 1, so we get 
