Question

How can you find the slope and intercept of $\dfrac{3}{4}x - y = 4$?

Answer 1

Since we need to find the slope and intercept so we need to convert the equation into slope-intercept form by solving $y$and any linear equation has the form of $y = mx + c$ where $m$ stands as slope which can be found by finding two distinct points and $c$ is the $y$ intercept where graph hits $y$ axis.

Formula used:
Since slope $m$ depicts how steep the line is with respect to horizontal. So if in the line two points found are $({x_1},{y_1})$ and $({x_2},{y_2})$ so slope comes out to be
$m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$
The point where line crosses why $y$ axis is the $y$ intercept $c$

Complete step by step solution:
As the given equation is $\dfrac{3}{4}x - y = 4$
Since we know that $y = mx + c$ is the slope intercept form of a line where $m$ is equal to slope and $c$is the $y$ intercept
So here we will subtract $\dfrac{3}{4}x$ from each side of equation

$$\Rightarrow \dfrac{3}{4}x - \dfrac{3}{4}x - y = - \dfrac{3}{4}x + 4 \\\ \Rightarrow - y = - \dfrac{3}{4}x + 4 \\\$$

Now after dividing $- 1$ from both sides we will get
$y = \dfrac{3}{4}x + ( - 4)$
So we will find that slope is $m = \dfrac{3}{4}$ and $c$ be the $y$ intercept is $- 4$
Now we will plot the graph

Additional Information:
Keep in mind that slopes can be negative or positive. Here y will tell how far a line goes, x tells us how far along it goes, m tells about the slope and c is the intercept where the lines crosses y axis

Note: While solving the above equation we need to convert the equation given in the slope intercept form and later on after finding the value of $m$ and $c$ then pick a point on line and check if it satisfies the equation by plugging it in. So $x$ intercept is $\left( {\dfrac{{16}}{3},0} \right)$ and $y$ intercept is $(0, - 4)$ which mean line cuts $y$ axis at $- 4$