Question

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

Answer 1

Hint: We are given an equation of line and we have to find its slope and y-intercept. The equation we are given is of the form $ y=mx+c $ . As it is already into the slope intercept form of line $ y=mx+c $ . Here m is the slope and c is the y-intercept. In comparison with the given equation with this standard form we can easily find the slope and Y-intercept of the line.

Complete step by step answer:
Step1:
We are given an equation of the line $ y = \dfrac{{ - 3}}{4}x + 3 $ . The equation is already in the slope intercept form. So using the standard form of the equation i.e. y=mx+c. Here m is the slope and c is the y-intercept.

Step2:
Now we will compare the equation with y=mx+c and in comparison we will find that here $ m = \dfrac{{ - 3}}{4} $ ; $ c = 3 $ .

Hence the slope is $ \dfrac{{ - 3}}{4} $ and y-intercept is $ 3 $

Additional information:
The slope of the line can also be determined by the formula if two coordinates are given.
 $ m=\dfrac{y_2 - y_1}{x_2 - x_1}$
Here $ y_2 $ and $ y_1 $ are the y coordinates and $ x_1 $ and $ x_2 $ are the $ x $ coordinates.

Note: In such types of questions students didn’t get an approach how to solve the question. They get confused by seeing the equation of how to find the slope and intercept. But when the equation is given then just compare it with the slope intercept form i.e. $ y=mx+c $ . And we can easily find the slope and y-intercept. Sometimes equations are already given in the form y=mx+c. And if it is not given then it can be converted into the slope- intercept form. And then we can easily find the slope and intercept on comparison.