Question

# Show m = 2 for the straight line 8x - 4y = 12.

Hint:

### We need to verify the value of m for an equation of straight line. We take the help of slope intercept form of equation of a line and convert the given equation in the form y = mx + c. Then we compare both the equations to find the value of m and check if it is equal to the given value.

## The correct answer is: m = 2 for the straight line 8x - 4y = 12

### Step by step solution:

The slope/ gradient of a line is denoted by m.

The given equation of the line is

8x - 4y = 12

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 8x - 4y = 12, as below

-4y = -8x - 12

Dividing the above equation by (-4) throughout, we get

Simplifying, we have

y = 2x + 3

Comparing with y = mx + c, we get that m = 2

Thus, m = 2 for the straight line 8x - 4y = 12

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 8x - 4y = 12, as below

Dividing the above equation by (-4) throughout, we get

Simplifying, we have

Comparing with y = mx + c, we get that m = 2

Thus, m = 2 for the straight line 8x - 4y = 12

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 = 8, b = -4, so we get