Question

Find the equation (in slope-intercept form) of the line with the given slope that passes through the pointwith the given coordinates.slope::-5ordered pair: (-1,3)2

Answer 1

y = - 5/2 x + 1/ 2

Step-by-step explanation:

A linear equation in slope-intercept form is given by

`y=mx+b`

where m = slope and b = y-intercept.

Now in our case, we are told that our equation has a slope of -5/2. This means m = -5/2 and so we have

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

Furthermore, we are also told that the line defined by this equation passes through (-1, 3). This means that our equation must satisfy x = -1 when y = 3.

Putting x = -1 and y = 3 into the above equation gives

`3=-(5)/(2)(-1)+b`

Our goal now is to solve for b.

The negative signs on the right-hand side cancel to give

`3=(5)/(2)+b`

subtracting 5/2 from both sides gives

`3-(5)/(2)=(5)/(2)+b-(5)/(2)`
`3-(5)/(2)=b`

Since 3 - 5/2 = 1/2, the above becomes

`b=(1)/(2)`

Hence, the equation of our line in slope-intercept form is

`\boxed{y=-(5)/(2)x+(1)/(2)\text{.}}`