Question

3.a.Sketch a line through the point

(-2,5) such that as an x-value

increases by 3. the y-value

decreases by 2.

y

o

Answer 1

Explanation:

Let the equation of the line passing through a point (x', y') and slope 'm' is,

y - y' = m(x - x')

Since x-value increases by 3,

Δx = 3

And y-value decreases by 2,

Δy = -2

Therefore, slope =
`(\triangle y)/(\triangle x)`

Slope =
`-(2)/(3)`

Equation of the line passing through (-2, 5) and slope =
`-(2)/(3)` will be,

y - 5 =
`-(2)/(3)(x+2)`

y =
`-(2)/(3)x-(4)/(3)+5`

y =
`-(2)/(3)x+(11)/(3)`

y =
`(1)/(3)(-2x+11)`

Table for input-output values will be,

x -2 0 1 2 3

y 5 3.7 3 2.3 1.7

We can plot these points to get the line on a graph.