# Question #dff70

Jan 24, 2017

Solve the equation for $y$.

#### Explanation:

$- 4 x + 3 y = 21$

Add $4 x$ to both sides.

$3 y = 4 x + 21$

Divide both sides by $3$.

$y = \frac{4}{3} x + \frac{21}{3}$

Simplify.

$y = \frac{4}{3} x + 7$

Jan 24, 2017

We know that slope-intercept form is

$y = m x + c$
where $m$ is slope and $c$ is intercept on $y$-axis.

Let us convert given equation $- 4 x + 3 y = 21$ in the above form by keeping $y$ term on LHS and all taking remaining terms to RHS.
$\implies 3 y = 4 x + 21$
Dividing both sides by $3$, we get

$\frac{3 y}{3} = \frac{4 x + 21}{3}$
$y = \frac{4}{3} x + 7$
is the required form.

If we plot this equation with inbuilt graphic tool we get the following:

Slope$= \frac{\Delta y}{\Delta x} = \frac{7}{5.25} = \frac{7}{5.25} \times \frac{4}{4} = \frac{28}{21} = \frac{4}{3}$
Intercept on $y$axis$= 7$