Question

A line passes through (2, -7) and (-3, 3). Find the slope-intercept form of the equation of the line.Then fill in the value of the slope, m, and the value of the y-intercept, b, below. mb

Answer 1

We are given the points (2,-7) and (-3,3) to find the equation of the line that passes through them. Recall that the slope-intercept form of the line equation is of the form

`y=mx+b\text{ }`

where m is the slope and b is the y-intercept.

We can calculate the slope m as follows: Given points (a,b) and (c,d) the slope of theline that passes through them is given by the formula

`m=\frac{d\text{ -b}}{c\text{ -a}}=\frac{b\text{ -d}}{a\text{ -c}}`

In our case we have a=2, b=-7, c=-3 and d=3 So we get

`m=\frac{\text{ -7 -3}}{2\text{ -(-3)}}=\frac{\text{ -10}}{5}=\text{ -2}`

So, so far our equation looks like this

`y=\text{ -2x+b}`

note that we want that this line passes through the point (2, -7). So this means that if we replace x by 2 then y is -7. So we have the equation

`\text{ -7= -2}\cdot2+b=\text{ -4+b}`

So if we add 4 on both sides we havethat

`b=\text{ -7+4= -}3`

So our line equation would be

`y=\text{ -2x -3}`

and the values of m and b are -2 and -3 respectively.