Question

Find the gradient and the intercept shown by the straight line 2x + 3y = 6 ​

Answer 1

The gradient is -
`(2)/(3)` and the intercept is 2.

Explanation:

First, transform the given equation into the slope-intercept form, y = mx + b. The variable m represents slope (gradient) and the variable b represents the intercept.

2x + 3y = 6

3y = -2x + 6

y = -
`(2)/(3)`x + 2

The gradient is -
`(2)/(3)` and the intercept is 2.

Answer 2

`\sf gradient =(-2)/(3)\\\\ y -intercept = 2`

Explanation:

Equation of the line in slope intercept form:

`\sf \boxed{\bf y = mx +b}`

Here m is the slope or gradient and b is the y-intercept.

Write the given equation in slope-intercept form.

2x + 3y = 6

3y = -2x + 6

`\sf y =(-2)/(3)x +(6)/(3)\\\\ y = (-2)/(3)x + 2`

`\sf gradient =(-2)/(3)\\\\ y -intercept = 2`