Question

Which of the following is an equation for the line that passes through the point (0,0) and is perpendicular to the line shown above ?

Answer 1

A. y =
`(5)/(4)x`

Explanation:

The equation of a straight line is given as;

y = mx + c

where: m is the slope and c is the intercept

For the line to pass through points (0, 0), then intercept, c is zero.

So that, y = mx

From the graph, slope, m =
`(5)/(4)`

Therefore, the required equation is;

y =
`(5)/(4)x`

Answer 2

Option A.
`y=(5)/(4)x`

Explanation:

step 1

Find the slope of the line shown in the graph

The given line pass through the points (0,3) and (5,-1) (see the graph)

The formula to calculate the slope between two points is equal to

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

substitute the values

`m=(-1-3)/(5-0)`

`m=(-4)/(5)`

`m=-(4)/(5)`

step 2

Find the slope of the line perpendicular to the line shown in the graph

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

`m_1*m_2=-1`

we have

`m_1=-(4)/(5)` ---> slope of the line shown in the graph

substitute

`(-(4)/(5))*m_2=-1`

therefore

`m_2=(5)/(4)`

step 3

Find the equation of the line that passes through the point (0,0) and is perpendicular to the given line in the graph

we have

`m=(5)/(4)`

`point\ (0,0)`

Remember that

If a line pass through the origin, then represent a proportional relationship

The linear equation is equal to
`y=mx`

substitute

`y=(5)/(4)x`