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