Math Problem Statement

write an equation in standard form of the line shown (- 4 3 (- 5 2

Solution

It seems like you're describing two points, but the notation is a bit unclear. Based on your message, I assume you're referring to the points (-4, 3) and (-5, 2). If that's correct, let's go ahead and write the equation of the line in standard form using these two points.

Step-by-Step Solution:

  1. Identify the two points: The points are (4,3)(-4, 3) and (5,2)(-5, 2).

  2. Find the slope (mm): The slope formula is: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} Plugging in the coordinates of the points: m=235(4)=11=1m = \frac{2 - 3}{-5 - (-4)} = \frac{-1}{-1} = 1 So, the slope m=1m = 1.

  3. Use the point-slope form of the line equation: The point-slope form of the equation is: yy1=m(xx1)y - y_1 = m(x - x_1) Using point (4,3)(-4, 3) and slope m=1m = 1, we get: y3=1(x+4)y - 3 = 1(x + 4)

  4. Simplify to slope-intercept form: Distribute the slope: y3=x+4y - 3 = x + 4 Then, solve for yy: y=x+7y = x + 7

  5. Convert to standard form: To write the equation in standard form Ax+By=CAx + By = C, move all terms to one side: yx=7y - x = 7 Multiply through by 1-1 to make the coefficient of xx positive: xy=7x - y = -7

So, the equation of the line in standard form is: xy=7x - y = -7

Let me know if you'd like more details on any step, or if this is what you were looking for!


Related Questions:

  1. How do you find the slope when two points are given?
  2. What is the difference between slope-intercept form and standard form of a line?
  3. How do you graph the equation xy=7x - y = -7?
  4. What are the characteristics of parallel lines in terms of their slopes?
  5. How can you convert from point-slope form to standard form?

Tip: Always check the sign of your slope before converting to different forms to ensure consistency in the final equation!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Coordinate Geometry

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)
Point-slope form: y - y1 = m(x - x1)
Standard form: Ax + By = C

Theorems

Equation of a Line Theorem

Suitable Grade Level

Grades 8-10