Question

Find the equation (in terms of x) of the line through the points (-4,-5) and (1,5)

Answer 1

Step 1: Find the slope of the line:

Given the points (X1, Y1)=(-4,-5) and (X2, Y2)= (1,5), we have that the slope of the line that passes through the points (-4,-5) and (1,5) is:

`m=(Y2-Y1)/(X2-X1)=(5+5)/(1+4)=(10)/(5)=2`

Step 2: Write the provisional equation of the given line. If the slope of the line is m=2, we get that the provisional equation of this line is:

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

Step 3: Find the y-intercept b. Take any point (x,y) on the line and replace its coordinates into the above equation and then solve for b. For example, take the point (x,y)=(1,5), then we obtain:

`5\text{ =2(1)+b}`

this is equivalent to:

`5\text{ =2+b}`

solving for b, we get:

`b\text{ = 5-2 = 3}`

that is:

`b\text{ = 3}`

Step 4: Write the equation of the line. If the given line has slope m=2 and y-intercept b = 3, then its equation would be:

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

and in terms of x, this is equivalent to:

`f(x)=2x+3`

So that, we can conclude that the correct answer is:

`f(x)=2x+3`