Points M(2, 3) and N(x, -6) lie on the same line. Theline also passes through the origin.3A. For a line passing through the origin, what do younotice about measuring rise over run from the originto another point on the line?/М(2, 3)B. Find the rise over run from the origin to Point M.088N(x, -6)riserunC. The rise-over-run ratio, or slope, of any line is constant. Use thisratio to write an equation that can help you find the x-coordinate ofPoint N.- 0D. Use proportional reasoning to solve for x.X =Turn and Talk Explain, using the rise and the run, why the slope of ahorizontal line is 0.Check Understanding1. Explain how dilation scale factors can help you identify points on a linepassing through the origin given one additional point.nr ydibicos2. A line passes through the origin and (5, 3). Identify two additional pointson this line.140

Points M(2, 3) and N(x, -6) lie on the same line. The line also passes through the origin. A. For a line passing through the origin, what do you notice about measuring rise over run from the origin to another point on the line? М(2, 3) B. Find the rise over run from the origin to Point M. 888 N(x, -6) rise run C. The rise-over-run ratio, or slope, of any line is constant. Use this ratio to write an equation that can help you find the x-coordinate of Point N. 0- x -0 D. Use proportional reasoning to solve for x. X =

Points M(2, 3) and N(x, -6) lie on the same line. The line also passes through the origin. A. For a line passing through the origin, what do you notice about measuring rise over run from the origin to another point on the line? М(2, 3) B. Find the rise over run from the origin to Point M. 888 N(x, -6) rise run C. The rise-over-run ratio, or slope, of any line is constant. Use this ratio to write an equation that can help you find the x-coordinate of Point N. 0- x -0 D. Use proportional reasoning to solve for x. X =

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Concept explainers

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

Question

Points M(2, 3) and N(x, -6) lie on the same line. The
line also passes through the origin.
3
A. For a line passing through the origin, what do you
notice about measuring rise over run from the origin
to another point on the line?
/М(2, 3)
B. Find the rise over run from the origin to Point M.
088
N(x, -6)
rise
run
C. The rise-over-run ratio, or slope, of any line is constant. Use this
ratio to write an equation that can help you find the x-coordinate of
Point N.
- 0
D. Use proportional reasoning to solve for x.
X =
Turn and Talk Explain, using the rise and the run, why the slope of a
horizontal line is 0.
Check Understanding
1. Explain how dilation scale factors can help you identify points on a line
passing through the origin given one additional point.
nr yd
ibicos
2. A line passes through the origin and (5, 3). Identify two additional points
on this line.
140

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