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 .