Question

work out the equation of the line which has a gradient of 3 and pases trouthg the point -1 ,3

Answer 1

Answer:

y = 3x + 6

Explanation:

The basic equation to represent a line is:

$y = mx +b$

Where m is the value of the slope or gradient of it.

We are told that the gradient is 3. That means,

$m = 3$

In the equation, b represents the intercept with the y-axis. To find it, we can use the point given in the following way:

$y = mx + b \\ 3 = 3( - 1) + b \\ 3 = - 3 + b \\ 3 + 3 = b \\ 6 = b$

Why can we do that? Every point that belongs to a certain line can be obtained through its formula, therefore, we can replace the values of the coordinates of the point (3 in y and -1 in x) to find the value of b.

Finally, with the value of the slope and the intercept with the y-axis, we can write the equation of the line as:

$y = 3x + 6$