Question

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

Answer 1

In this problem we have been given a linear equation. And we are asked to find the slope and $y -$ intercept of the given linear equation. To find the slope and $y -$ intercept of the given linear equation we need to use slope intercept form. In that slope intercept form, there will be $x$ term and the coefficient of $x$ is the slope and also there will be a constant term and the constant term is the $y -$ intercept of the given linear equation.

Formula used: The slope intercept form is $y = mx + b$ , where $m$ is the slope of a given linear equation and $b$ is the $y -$ intercept .

Complete step by step answer:
Given linear equation is $y = - \dfrac{3}{4}x + 3$
One of the equations of a straight line is $y = mx + b$ often referred to as the slope intercept form.
Use the slope intercept form to find the slope and $y -$ intercept
The slope intercept form is $y = mx + b$ , where $m$ is the slope of a given linear equation and $b$ is the $y -$ intercept.
Now, let’s compare the given linear equation with the slope intercept form, we get,
$m = - \dfrac{3}{4}$ and $b = 3$
The slope of the line is the value of $m$ and the $y -$ intercept is the value of $b$ .

Therefore, slope $= - \dfrac{3}{4}$ , $y -$ intercept $= 3$.

Note: We can rewrite the given equation as $\dfrac{3}{4}x + y = 3$ . We can also find the slope of the given linear equation by comparing the given line equation with $ax + by = c$ and then we write the values of $a,b,c$. In such cases the formula to be used to calculate slope is $- \dfrac{a}{b}$ . Now, substitute the values of $a,b$ in the formula, the value of slope is $\dfrac{{\dfrac{{ - 3}}{4}}}{1}$ this can be written as $\dfrac{{ - 3}}{4} \times \dfrac{1}{1}$ . Multiplication of any number with $1$ is again the number itself. So, the slope value is $\dfrac{{ - 3}}{4}$ .
Now, to find the y-intercept, we can put $x = 0$ .
$\dfrac{3}{4} \times 0 + y = 3$
Hence, we get $y = 3$ . This is the y-intercept.