Question

Find an equation for the line that passes through the points −5, 1 and −1, 2.

Answer 1

y= 0.25x + 2.25

Explanation:

To find the equation of the line we must use y=mx+c where m is the gradient and c is the y intercept.

We need to find the gradient and y-intercept to construct an equation. To find the gradient we can use the formula m=
`(y2-y1)/(x2-x1)` I will take y1 as 1 and y2 as 2. You can use the opposite also y1 as 2 and y2 as 1.

m= (2-1)/(-1-(-5))= 0.25

We have the gradient but we don't have the y-intercept. We can find it by taking any one of the coordinates and plugging all the values we have into y=mx+c. I will take the 1st coordinate.

y= 0.25x + c

1= 0.25(-5) + c

1= -1.25 + c

c= 1+1.25= 2.25

Now plug in the values of the gradient and y-intercept into y=mx+c.

y= 0.25x + 2.25

Answer 2

4 y = x + 9.

Explanation:

Let the point A be (-5, 1) and point B be (-1, 2).

The slope of the straight line passing through A and B is given by:

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

= (2-1)/(-1-(-5)) = 1/4.

Equation of the straight line that passes through A(-5,1) and has a slope of 1/4 is given by

y - 1 = 1/4 × (x +5)

=> y = 1+5/4 +x/4

=> 4 y = x + 9.