Answered

Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

For each part, use the equation [tex]4x + 3y = -12[/tex], where [tex]x[/tex] and [tex]y[/tex] are real numbers.

(a) Graph the equation on the grid provided.

(b) Give three solutions to the equation.

(i) [tex]\((3, 0)\)[/tex]

(ii) [tex]\((x_1, y_1)\)[/tex]

(iii) [tex]\((x_2, y_2)\)[/tex]

Sagot :

GinnyAnswer
Sure, I'll guide you through the steps required to solve each part of the question using the equation [tex]\(4x + 3y = -12\)[/tex].

### Part (a): Graph the equation on a coordinate grid

1. Rewrite the Equation:
It's often helpful to rewrite the equation in slope-intercept form [tex]\(y = mx + b\)[/tex], but we'll keep it in its given form for plotting:
[tex]\[4x + 3y = -12\][/tex]

2. Find Intercepts:
- x-intercept (where [tex]\(y = 0\)[/tex]):
[tex]\[4x + 3(0) = -12 \Rightarrow 4x = -12 \Rightarrow x = -3\][/tex]
So, the x-intercept is [tex]\((-3, 0)\)[/tex].
- y-intercept (where [tex]\(x = 0\)[/tex]):
[tex]\[4(0) + 3y = -12 \Rightarrow 3y = -12 \Rightarrow y = -4\][/tex]
So, the y-intercept is [tex]\((0, -4)\)[/tex].

3. Plot Points and Draw Line:
- Plot the intercepts [tex]\((-3, 0)\)[/tex] and [tex]\((0, -4)\)[/tex] on the grid.
- Draw a straight line through these points to represent the equation [tex]\(4x + 3y = -12\)[/tex].

### Part (b): Give Three Solutions to the Equation

1. Point (0, -4):
- From the intercepts calculated above, we know that [tex]\((0, -4)\)[/tex] is a solution.

2. Point (3, -8):
- Substitute [tex]\(x = 3\)[/tex] into the equation:
[tex]\[4(3) + 3y = -12\][/tex]
[tex]\[12 + 3y = -12\][/tex]
[tex]\[3y = -24\][/tex]
[tex]\[y = -8\][/tex]
- So, [tex]\((3, -8)\)[/tex] is a solution.

3. Point (-3, 0):
- From the intercepts calculated above, we know that [tex]\((-3, 0)\)[/tex] is also a solution.

### Summary

- Three solutions for the equation [tex]\(4x + 3y = -12\)[/tex] are:
- [tex]\((0, -4)\)[/tex]
- [tex]\((3, -8)\)[/tex]
- [tex]\((-3, 0)\)[/tex]

These points all lie on the line represented by the equation, and you should graph the line by plotting these points and drawing a line through them.
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.