Question

# The coordinate A=(0,2) lies on a straight line. The gradient of the line is 5 . Using this information, state the equation of the straight line.

Hint:

### We are given the slope of a line and a point which lies on the straight line. To find the equation of the line, we use the point slope form of the equation which is given by y - b = m(x - a), where m is the slope and (a, b) is the point lying on the plane. We simplify this equation and bring it to the general form which is ax + by + c = 0

## The correct answer is: 5x - y + 2 = 0

### Step by step solution:

Given,

Slope/ Gradient of the line (m) = 5

Let (a, b) denote the point A lying on the plane.

Then (a, b) = (0, 2)

We know that, the equation of a line with slope m and passing through the point (a, b) is given by

y - b = m(x - a)

Putting the values of m and (a, b) in the above equation, we get

y - 2 = 5(x - 0)

Simplifying, we have

y - 2 = 5x

Taking all the terms on one side and rewriting the above equation, we have

5x - y + 2 = 0

This is the required equation of the line.

We know that, the equation of a line with slope m and passing through the point (a, b) is given by

Putting the values of m and (a, b) in the above equation, we get

Simplifying, we have

Taking all the terms on one side and rewriting the above equation, we have

This is the required equation of the line.

The student needs to remember all the different forms of equation of a line and what each term and notation signifies in the equation.

Other forms of the equation of a line are, slope intercept form, axis intercept form, normal form, etc.