Question

The equation of a line is given by, 13x – y + 12 = 0. Find the slope and both the intercepts.​

Answer 1

The slope is 13.

The x intercept is
`x=(-12)/(13)`.

The y intercept is
`y=12`.

Explanation:

1. Finding the slope.

This is a linear equation, because it's graph forms a line. In a linear equation, the slope is always the value that multiplies x. In this case, x is being multiplied by 13, therefore, the slope is 13.

2. Finding the x intercept.

The x intercept is found when the value of y is 0. Let's replace the value of y for 0 in the equation and solve the x:

`13x-y + 12 = 0\\\\13x-(0) + 12 = 0\\\\13x+12 = 0\\\\13x= -12\\\\x=(-12)/(13)`

The x intercept is
`x=(-12)/(13)`.

3. Finding the y intercept.

The y intercept is found when the value of x is 0. Let's replace the value of x for 0 in the equation and solve the y:

`13x-y + 12 = 0\\\\13(0)-y + 12 = 0\\\\-y + 12 = 0\\\\-y=-12\\\\y=12`

The y intercept is
`y=12`.