Question

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

Answer 1

Answer:

$\sf gradient =\dfrac{-2}{3}\\\\ y -intercept = 2$

Step-by-step 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

            $\sf y =\dfrac{-2}{3}x +\dfrac{6}{3}\\\\ y = \dfrac{-2}{3}x + 2$

$\sf gradient =\dfrac{-2}{3}\\\\ y -intercept = 2$

Answer 2

Answer:

The gradient is -$\frac{2}{3}$ and the intercept is 2.

Step-by-step 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 = -$\frac{2}{3}$x + 2

The gradient is -$\frac{2}{3}$ and the intercept is 2.