Question

Write the given equation of the line in the slope intercept form from the point slope form $y - 4 = \dfrac{3}{4}\left( {x + 8} \right)$ .

Answer 1

The general form of the point slope form for linear equations is $y - {y_1} = m\left( {x - {x_1}} \right)$, this form determines the slope and point of the line and the general form of the slope intercept form is $y = mx + c$ , this form determines the slope and the y-intercept of the line.

Complete step by step solution:
In this problem, we have given an equation in the point slope form and we have to write it in the slope intercept form and the equation given is
$\Rightarrow y - 4 = \dfrac{3}{4}\left( {x + 8} \right)$
And now, we will use the distributive property to solve further,
$\Rightarrow y - 4 = \dfrac{3}{4}x + \dfrac{3}{4} \times 8$
On further solving, we get,
$\Rightarrow y - 4 = \dfrac{3}{4}x + 3 \times 2 \\\ \Rightarrow y - 4 = \dfrac{3}{4}x + 6 \\\$
Now, we will add$4$ on both sides of the equation,
$\Rightarrow y - 4 + 4 = \dfrac{3}{4}x + 6 + 4$
On adding, we get,
$\Rightarrow y = \dfrac{3}{4}x + 10$
And on comparing the above equation with the general form of the slope intercept form, we will find that both the equations are familiar to each other and hence, the slope intercept form of the given equation is $y = \dfrac{3}{4}x + 10$.

Note: In this problem, we have used the distributive property to solve the equation. The general form of the distributive property is $a\left( {b + c} \right) = a \times b + a \times c$, where these type of equations are given then we have to use this property, it is also known as distributive law of multiplication. According to this property, if the numbers given in the parentheses are added and then multiplied with the number given outside is same when the number given inside the parentheses are multiplied with the term given outside the parentheses individually.