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Chapter 13: Q32. (page 534)

A line passes through points (-2, -1) and (4, 3). Where does the line intersect the x-axis? the y-axis?

Short Answer

Expert verified

The required point of intersection of line withx−axis   is  (−12,0)  and  y−axis  is  (0,13)

Step by step solution

01

Step-1 – Given

Given that a line passes through points(−2,−1) and(4,3) .

02

Step-2 – To determine

We have tofind the point of intersection of line withx-axis and y-axis.

03

Step-3 – Calculation 

The two-point formula using these two points(x1,y1)  and  (x2,y2) is:

y−y1=y2−y1x2−x1(x−x1)

The given points are (−2,−1)and(4,3) .

y−(−1)=3−(−1)4−(−2)(x−(−2))y+1=23(x+2)3y+3=2x+43y−2x=1

The equation of the x-axis is y = 0, we solve it with3y−2x=1 .

3y−2x=13(0)−2x=1−2x=1x=−12

Equation of the y-axis is x = 0, solving it with3y−2x=1 .

3y−2x=13y−2(0)=13y=1y=13

So, the required point of intersection of line withx−axis   is  (−12,0).

  and  y−axis  is  (0,13)

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Most popular questions from this chapter

10. Find the distance between the points named. Give all answers in simplest

form.

  1. (0, 0) and (5, -3).
  2. (3, -2) and (-5, -2).
  3. (4, 4) and (-3, -3).

10. Find the distance between the points named. Give all answers in simplest

form.

  1. (0, 0) and (5, -3).
  2. (3, -2) and (-5, -2).

3. (4, 4) and (-3, -3).

In Exercises 16-19 a point P on a line and the slope of the line are given. Sketch the line and find the coordinates of two other points on the line.

P(2, 4); slope =−32.

A ine through H(3, 1) and J(5, a) has positive slope and makes a 60° angle measured counterclockwise with the positive x-axis. Find the value of a.

Find the distance between the two points. If necessary, you may draw graphs but you shouldn’t need to use the distance formula.

  1. (3, 3) and (-2, 3)
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