Question

Find the equation of the line.

Answer 1

y=1/2 +1.5

Explanation:

y intercept = 1.5

gradient = rise over run = 1/2

y = 1/2 +1.5

Answer 2

`y=(1)/(2)x+(3)/(2)`

Explanation:

Slope-intercept form:
`y=mx+b` when
`m` is the slope and
`b` is the y-intercept (the y-coordinate of the point where the line crosses the y-axis)

1) Find the slope (
`m`)

`m=(y_2-y_1)/(x_2-x_1)` when the given points are
`(x_1,y_1)` and
`(x_2,y_2)`

We can use any two points on the line to plug into this equation, but it's often easiest to use points that have whole-number coordinates. For example, we can use the points (1,-1) and (3,0).

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

Two negatives make a positive

`m=(0+1)/(3-1)\\m=(1)/(2)`

So far, our equation looks like this:

`y=(1)/(2)x+b`

2) Find the y-intercept (
`b`)

We're told to approximate the y-intercept based on what appears to be true in the graph. In the graph, we can see that the y-intercept appears to occur when y=-1.5, or when y=
`-(3)/(2)`. Therefore,
`b=(-3)/(2)`.

Now, after plugging both
`m` and
`b` into our equation, our final equation looks like this:

`y=(1)/(2)x+(3)/(2)`

I hope this helps!