Question 1171592: I need help writing an equation for this graph please.
https://imgur.com/a/bKYs8v2 Found 2 solutions by math_tutor2020, MathTherapy:Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
The two blue points indicated on the line are (0,-4) and (3,-7). You can pick any two points on the blue line, but I'll pick these two as they stand out more.
Use the slope formula to get
note how we subtract the y values up top, and subtract the x values in the same order down below
The slope is -1.
A slope of -1 means each time we move down 1, we move to the right 1.
We could say
slope = rise/run = -1/1
to be more thorough
rise = -1 means we move down 1
run = 1 means we move to the right 1
The y intercept is where the graph crosses the y axis. Visually this is shown as (0,-4) so b = -4 is the y intercept.
If we didn't have this point, we could plug either point into y = mx+b, along with the slope we just found, to solve for b.
So if we tried (x,y) = (0,-4) and m = -1, then,
y = mx+b
-4 = (-1)(0)+b
-4 = 0+b
-4 = b
b = -4
or we could try (x,y) = (3,-7) and m = -1
y = mx+b
-7 = (-1)*(3)+b
-7 = -3+b
-7 = b-3
b-3 = -7
b-3+3 = -7+3 ... adding 3 to both sides
b = -4
Either way we get the same y intercept value.
To wrap things up, we found
m = -1 = slope
b = -4 = y intercept
Therefore, we go from
y = mx+b
to
y = -1x+(-4)
This can be simplified to y = -x-4
As a way to check, plug in x = 0 and you should get y = -4. This is the point (0,-4). Also, plugging in x = 3 should lead to y = -7. This is the point (3,-7).
2 points shown: (0, - 4) and (3, - 7)
m, or slope:
Slope-intercept form of a linear equation: y = mx + b
With a slope of - 1, and y-intercept, (0, - 4), equation is: