Math Problem Statement

what type of slope the Line has.(3,5) and (-1,2)

Solution

To find the slope of a line passing through the points (3,5)(3, 5) and (1,2)(-1, 2), we use the slope formula:

m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

Where:

  • (x1,y1)(x_1, y_1) = (3,5)(3, 5)
  • (x2,y2)(x_2, y_2) = (1,2)(-1, 2)

Now, substituting the coordinates into the formula:

m=2513=34=34m = \frac{2 - 5}{-1 - 3} = \frac{-3}{-4} = \frac{3}{4}

Thus, the slope of the line is 34\frac{3}{4}, which means the line rises 3 units for every 4 units it moves horizontally to the right.

Do you want a more detailed explanation or have any questions?

Here are some related questions you might find interesting:

  1. How do you determine if the line is increasing or decreasing based on its slope?
  2. What happens if the slope is negative?
  3. How can the slope formula be used to find the equation of a line?
  4. What is the slope of a horizontal and vertical line?
  5. How do you graph a line if you know its slope and a point on the line?

Tip: When calculating slope, always pay attention to the order of the points you subtract. It can affect the sign of your slope.

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Math Problem Analysis

Mathematical Concepts

Slope
Linear Equations

Formulas

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

Theorems

Slope of a line between two points

Suitable Grade Level

Grades 7-9