Math Problem Statement

1-week streak. 1

Level 6 2 /6 skills

You might need: Calculator Problem A coordinate plane. The x- and y-axes each scale by one. A graph of a line intersects the points negative one, zero and zero, one. [\small{1}] [\small{2}] [\small{3}] [\small{4}] [\small{\llap{-}1}] [\small{\llap{-}2}] [\small{\llap{-}3}] [\small{\llap{-}4}] [\small{1}] [\small{2}] [\small{3}] [\small{4}] [\small{\llap{-}1}] [\small{\llap{-}2}] [\small{\llap{-}3}] [\small{\llap{-}4}] [y] [x] What is the slope of the line?

Solution

To find the slope of a line, you can use the slope formula:

slope=y2−y1x2−x1\text{slope} = \frac{{y_2 - y_1}}{{x_2 - x_1}}

The problem tells us that the line intersects the points (−1,0)(-1, 0) and (0,1)(0, 1). Let’s substitute these points into the slope formula, where (x1,y1)=(−1,0)(x_1, y_1) = (-1, 0) and (x2,y2)=(0,1)(x_2, y_2) = (0, 1).

slope=1−00−(−1)=11=1\text{slope} = \frac{{1 - 0}}{{0 - (-1)}} = \frac{1}{1} = 1

So, the slope of the line is 11.

Do you want more details or have any questions?
Here are 5 related questions to consider:

  1. How would the slope change if the points were (−2,−1)(-2, -1) and (1,2)(1, 2)?
  2. What is the equation of the line passing through (−1,0)(-1, 0) and (0,1)(0, 1)?
  3. Can you find the y-intercept of a line given its slope and a point?
  4. How do parallel and perpendicular lines relate to their slopes?
  5. What happens to the slope if the line is vertical?

Tip: For any two points on a line, the slope represents how much the y-coordinate changes for a unit change in the x-coordinate.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Coordinate Geometry

Formulas

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

Theorems

Slope-Intercept Theorem

Suitable Grade Level

Grades 6-8

Related Recommendation

Finding the Slope of a Line Between Two Points (-1, 0) and (-2, -5)

Find the Slope of a Line through Points (4, -1) and (6, 1)

Find the Slope of the Line through Points (5, 4) and (6, 1)

Find the Slope of the Line Through Points (7, -5) and (3, -1)

Find the Slope of a Line Through Points (4, -1) and (2, 3)