Respuesta :
Answer:
[tex]3x - 4y = -12[/tex]
Step-by-step explanation:
In this problem, we are given two values: the x-intercept and the slope of this equation. There are two methods for solving equations like this: the point-slope and slope-intercept forms. After using those two methods, we can flip this relationship into standard form.
Let us define what the x-intercept of a line is. In an x-intercept scenario, the y-coordinate will always be zero, no matter what. So, we can set up an ordered pair that showcases this x-coordinate's use, [tex](-4, 0)[/tex], which we can define as our [tex](x_{1}, y_{1})[/tex] for our point-slope form equation. Speaking of which, let's substitute these values into it!
[tex]y - y_{1} = m(x - x_{1})\\ y - 0 = \frac{3}{4}(x - (-4)\\ y = \frac{3}{4}(x + 4)[/tex]
We have just finished setting up this system of equations which brought us into simplifying the slope-intercept form of this equation. By doing so, we can replace said variables with the values above, and eventually put it into standard form!
Getting rid of the fractions, we get.
[tex]4y = 3(x + 4)\\ 4y = 3x + 12[/tex]
Now, we finally have our equation! Let us separate the constants and the coefficient variables, and we have our standard-form equation!
[tex]4y = 3x + 12\\ 3x - 4y + 12 = 0\\ 3x - 4y = -12[/tex]
There you have it! Now we have simplified this word problem into a standard-form equation.
I hope this helps!
