Math Problem Statement

Find y if the slope of the line segment joining (3, 2) to (4, y) is -3.

Solution

To find yy, we use the formula for the slope of a line segment that passes through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2):

slope=y2y1x2x1\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}

Here, the points given are (3,2)(3, 2) and (4,y)(4, y). So,

(x1,y1)=(3,2),(x2,y2)=(4,y)(x_1, y_1) = (3, 2), \quad (x_2, y_2) = (4, y)

The slope is given as 3-3. Substituting the values into the slope formula:

3=y243-3 = \frac{y - 2}{4 - 3}

Simplify the denominator:

3=y2-3 = y - 2

To solve for yy, add 2 to both sides:

y=3+2y = -3 + 2

y=1y = -1

So, the value of yy is 1-1.

Would you like more details or have any questions?

Here are some related questions:

  1. What is the formula for finding the slope between two points?
  2. How do you find the equation of a line given a point and the slope?
  3. How can you determine if two lines are parallel?
  4. What does a negative slope indicate about the direction of a line?
  5. How can you find the midpoint of a line segment joining two points?

Tip: When dealing with slope, always pay attention to the signs to determine the direction of the line.

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Math Problem Analysis

Mathematical Concepts

Algebra
Coordinate Geometry
Slope of a Line

Formulas

Slope formula: (y2 - y1) / (x2 - x1)

Theorems

Slope Theorem

Suitable Grade Level

Grades 8-10