Question

Equation of the Line

Lesson
I
After going through this lesson, you are expected to find the equation of a
line given (a) two points, (b) the slope and a point and (c) the slope and its
intercepts
From the given linear equation, we can determine 2 points that will satis-
fy the equation. Also we can determine the slope and the y- intercept so as the
x and y intercepts.
Example: Given - 2x + y = 6
Find: a. two points that will satisfy the equation
(b) slope and y-intercept
(c) x and y intercept
Solution:
(a) -2x + y = 6
If x = -1
If y = 2
-21-1) + y = 6
- 2x + 2 = 6
2 + y = 6- y = 4
-2x = 4-x= -2
The point is (-1,4)
The point is (-2, 2)
(b) Change the equation to slope intercept form : y = 2x + 6
Therefore the slope m = 2 and the y-intercept b = 6
(c) Find the and y intercept of -2x + y = 6
Let x = 0, -2(0) + y = 6; y = 6. the intercept is (0,6)
Let y = 0, -2x + 0 = 6; -2x = 6, X = -3, the y intercept is (-3,0)
Learning Task 1 : From the given equation of the line a) find two points that will
satisfy the equation, b) the slope and the y intercepts and c) the x and y-
intercepts.
2.
3y - X9
1. 3x + 2y = 5​

Answer 1

9514 1404 393

Answer:

a) (0, 5/2), (5/3, 0)

b) m = -3/2; b = 5/2

c) (5/3, 0), (0, 5/2)

Explanation:

Given:

3x +2y = 5

Find:

a) two points that satisfy the equation

b) slope and y-intercept

c) x-intercept

Solution:

Since the intercepts are points on the line, finding them satisfies all parts of the question except finding the slope.

a) Let x=0. Then we can find y from ...

3·0 +2y = 5

y = 5/2

One point is (0, 5/2).

Let y=0. Then we can find x from ...

3x +2·0 = 5

x = 5/3

Another point is (5/3, 0).

Two points on the line are (0, 5/2) and (5/3, 0).

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b) The slope can be found using the slope formula on the two points we found.

m = (y2 -y1)/(x2 -x1)

m = (0 -5/2)/(5/3 -0) = -(5/2)/(5/3) = -3/2

The slope is -3/2. The y-intercept is 5/2.

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c) The x- and y-intercepts are (5/3, 0) and (0, 5/2), respectively.