Question

Find an equation for the line graphed below:

Answer 1

Answer given by bryc31 is correct:
`y = -(1)/(5)x -3` is correct

I am simply providing an explanation in case you need it

Explanation:

The slope-intercept form equation of a straight line in 2D coordinates is given by y = mx + b

where m is the slope(rise/run) and b the y-intercept i.e. the y value where the line intersects the y axis

Given two points (x₁, y₁) and (x₂, y₂) on the straight line, we can compute the slope as follows

m =
`(y_2 - y_1)/(x_2-x_1)`

Two distinct points on the line are at (0, -3) and (5,-4)

`m = (-4 -(-3))/(5-0) = (-4 + 3))/(5-0) = (-1)/(5) = - (1)/(5)`

So we know the equation to be

`y = - (1)/(5)x + b`

To find b, take any point on the straight line, plug in y and x values in the above equation and solve for b

However, looking at the graph we see that the line crosses the y axis at

y = -3. So this is the value for the y intercept i.e. b

The equation of the line is therefore

`y = - (1)/(5)x - 3`

Answer 2

Answer: y = -1/5x -3

Explanation: