Question

How do you write the equation $ y - 7 = - \dfrac{3}{4}(x + 5) $ in slope intercept form?

Answer 1

Hint: We have given an equation of a line as $ y - 7 = - \dfrac{3}{4}(x + 5) $ , which is a straight-line equation. A straight-line equation is always linear and represented as $ y = mx + c $ where $ m $ is the slope of the line and $ c $ is the y-intercept and $ \dfrac{{ - c}}{m} $ is the x-intercept .

Complete step-by-step answer:
The slope-intercept form of a line is represented as $ y = mx + c $ . In order to convert the given equation into this form, isolate the variable $ y $ and simplify the other side of the equation.
We have equation of line,
 $ y - 7 = - \dfrac{3}{4}(x + 5) $
Add $ 7 $ to both the side of the equation ,
 $ y = - \dfrac{3}{4}(x + 5) + 7 $
Now, open the parentheses as ,
 $ y = - \dfrac{3}{4}x - \dfrac{{15}}{4} + 7 $
Now, convert the equation as ,
 $ y = - \dfrac{3}{4}x - \dfrac{{15}}{4} + \dfrac{{28}}{4} $
Now, perform operations on like terms ,
 $ y = - \dfrac{3}{4}x + \dfrac{{13}}{4} $
Hence, we get the required result.
So, the correct answer is “ $ y = - \dfrac{3}{4}x + \dfrac{{13}}{4} $ ”.

Note: his type of linear equations sometimes called slope-intercept form because we can easily find the slope and the intercept of the corresponding lines. This also allow us to graph it.
We can quickly tell the slope i.e., $ m $ the y-intercepts i.e., $ (y,0) $ and the x-intercept i.e., $ (0,y) $ .we can graph the corresponding line .