# Question #5b70f

Feb 20, 2017

See explanation below.

#### Explanation:

Assuming the dot in $1.4$ is actually a decimal point, and not multiplication.

The general rule says that you can add/subtract the same number to/from both sides, or multiply/divide both sides by the same number and the equation will be equivalent (represents the exact same relationship between $x$ and $y$). Therefore:

$1.4 x - 4 y = 1 \implies 1.4 x \cancel{- 4 y} \cancel{+ 4 y} = 1 + 4 y$

$\implies 1.4 x - 1 = \cancel{1} + 4 y \cancel{- 1}$

$\implies 1.4 x - 1 = 4 y \implies 4 y = 1.4 x - 1$

First step, add $4 y$ to both sides, then subtract $1$ from both sides, and finally you can switch sides on equalities ($a = b \implies b = a$).

Slope-intercept form of a line

It's the form $y = a x + b$, where $a$ is the slope and $b$ the $y$-axis intercept (and none other, you need to have a $y$ without any coefficients). So, we need to take the equation we found, then divide everything by $4$:

$4 y = 1.4 x - 1 \implies y = \frac{\left(1.4 x - 1\right)}{4} \implies y = \left(0.35 x - 0.25\right)$. To graph this line, first write the equation in slope-intercept form. Then, simply pick any $x$ value other than zero, substitute it in the equation, then solve for $y$, then plot that point on the graph. That point is on the line. Then, notice that based on the slope-intercept form, $b = - 0.25 = - \frac{1}{4}$, so plot the point on the $y$ axis at $- \frac{1}{4}$ (that's what is meant by $y$ intercept).

Finally, connect both points and extend the line. The graph should look like this:

graph{y = 0.35x - 0.25 [-10, 10, -5, 5]}

---Side note---

If the $2.4$ on the second case you provided in the question is meant to be $1.4$, then the second case is not correct, since you can subtract $1.4 x$ from both sides, but you get a $\textcolor{red}{- 1.4 x} + 1$ instead of the $1.4 x + 1$.