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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 :

GinnyAnsweridn
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.
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