Question

How do you write $y - 7 = 4\left( {x + 4} \right)$ in standard form?

Answer 1

Hint: We are given an equation. Now, we have to find the standard form of the equation. First, we will apply the basic arithmetic operations to both sides of the equation. Then, rewrite the equation in the standard form.

Complete step by step solution:
We are given the equation, $y - 7 = 4\left( {x + 4} \right)$. First, we will simplify the expression on the right hand side of the equation.

Now, we apply distributive property at the right hand side.

$ \Rightarrow y - 7 = 4x + 16$

Now, we will subtract $y$ from both sides of the equation.

$ \Rightarrow y - 7 - y = 4x - y + 16$

On simplifying the expression, we get:

$ \Rightarrow - 7 = 4x - y + 16$

Now, we will subtract 16 from both sides of the equation.

$ \Rightarrow - 7 - 16 = 4x - y + 16 -16$

On simplifying the expression, we get:

$ \Rightarrow -23 = 4x - y$

Hence, the equation in standard form is $4x - y = - 23$

Note: The students must note that we basically first rewrite the equation given in slope-intercept form into standard form $Ax + By = C$ by rearranging the terms in the equation where A , B and C are positive integers. The linear equation in two variables can be written in two variables as $Ax + By = C$. The y-intercept is the value at which the x-coordinate is equal to zero. The value of the slope is equal to the change in y-coordinate to change in x-coordinate. Similarly, the value x-coordinate is determined by setting $y = 0$ in the equation. The equation of the line will pass through the point $\left( {x,y} \right)$. The equation of the straight line in two variables can be written in slope-intercept form as $y = mx + b$ where $m$ is the slope of the line and $b$ is the y-intercept.