Math Problem Statement

Solve the equation 3x + 4y + 5 = 0

Solution

The equation in the image is:

3x+4y+5=03x + 4y + 5 = 0

This is a linear equation in two variables, xx and yy. To simplify or rearrange this equation, we can express it in a more common form, such as slope-intercept form (y=mx+by = mx + b) or standard form (Ax+By=CAx + By = C).

Let’s first solve for yy:

3x+4y+5=03x + 4y + 5 = 0 Subtract 3x3x and 55 from both sides: 4y=3x54y = -3x - 5 Now, divide both sides by 4 to solve for yy: y=34x54y = -\frac{3}{4}x - \frac{5}{4}

This is the equation in slope-intercept form (y=mx+by = mx + b), where the slope m=34m = -\frac{3}{4} and the y-intercept b=54b = -\frac{5}{4}.

Would you like more details on this process or have any specific questions?

Here are five related questions:

  1. How do you graph the equation 3x+4y+5=03x + 4y + 5 = 0?
  2. What is the x-intercept of the equation 3x+4y+5=03x + 4y + 5 = 0?
  3. How do you convert the equation into standard form?
  4. What is the slope of the line represented by this equation?
  5. How can this equation be used to find points on the line?

Tip: When solving for yy in an equation, always try to isolate yy on one side to put the equation in a useful form, like the slope-intercept form.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Slope-intercept form: y = mx + b

Theorems

Linear equation theorem
Slope of a line

Suitable Grade Level

Grades 8-10