Question

Question 1 (Multiple Choice Worth 1 points)

(02.04 MC)
Choose the equation that represents a line that passes through points (-3, 2) and (2, 1).
5x + y = -13
5x - y = 17
Ox - 5y = -13
x + 5y = 7

Answer 1

x+5y = 7

Explanation:

The formula for finding the equation of a line is expressed as y= mx+c where;

m is the slope or gradient of the line defined as m = ∆y/∆x = y2-y1/x2-x1

Given the points (x1,y1) = (-3, 2) and (x2,y2) = (2, 1).

m = 1-2/2-(-3)

m = -1/5

To calculate the intercept c we will substitute any of the points given into the equation of the line to have;

y = mx+c

Using the point (-3,2)

Where x = -3, y=2

2 = (-1/5)(-3) + c

2 = 3/5+c

c = 2-3/5

c = 7/5

Substituting the value of m = -1/5 and c = 7/5 into the expression of equation of a line we have;

y = (-1/5)x+7/5

Multiplying through by 5 gives,

5y= -x+7

5y+x=7

= x+5y = 7 (D)

Answer 2

`x + 5y = 7`

Explanation:

Point A
`( x_(1) , y_(1) ) = (-3, 2)`

Point B
`( x_(2) , y_(2) ) = (2, 1)`

Now, slope of line passing through points (-3, 2) and (2, 1) :

`m = (y_(2) -y_(1) )/(x_(2)-x_(1) ) = (1 - 2)/(2 + 3) = (-1)/(5)`

Now equation of line having slope-intercept form where slope is m and c is y intercept, is y = mx + c,

By substituting the value of m in above equation,

`y = (-1)/(5)x + c`

`5y = -x + c` ...... (1)

Now since the line is passing through point (-3,2),therefore by substituting the value of x = -3 and y = 2 in above equation

`5 (2) = - (-3) + c`

`10 = 3 + c`

`c = 10 - 3 = 7`

Now by substituting the value of c in eq (1)

`5y = -x + c`

`5y = -x + 7`

On rearranging the above expression,

`x + 5y = 7`

Therefore option (4) is the correct answer.