Question

Please help me find the slope and y-intercept (50 point)

Answer 1

The slope is -5/4

The y-intercept is (0,4)

The equation of the line is y=-5/4x+4

Explanation:

First find two points. (0,4) and (4,-1)

The slope is change in y over change in x

(4-(-1))/(0-4)

5/-4

The slope is -5/4

The slope is the coefficient of x so the equation is y=-5/4x+b

Put in a point on the line for x and y. (0,4)

4=-5/4(0)+b

4=b

Put 4 in for b

y=-5/4x+b

The y intercept can be found by observation. The y intercept is where the line crosses the y axis where x=0

(0,4)

Answer 2

y= -5/4 x + 4

Explanation:

1. y-intercept (b) is found by looking at the graph, and it is at the point "y" where "x" equals zero, so the coordinate for this would be at (0,y). In this case it is (0,4). This means that the y-intercept is 4.

2. slope (m) is also found by looking at the graph, but takes a few more steps..

Firstly, we know that slope is expressed by m= Δy/Δx, or
`m=((y_2-y_1))/((x_2-x_1))`

If we plug in coordinates from the graph using two distinguished points (one we already know is (0,4) and the other is at the red dot (4,-1)) we can use the equation and find slope:

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

3. Now we can plug in these numbers into the equation y= mx + b, knowing that b is 4 and m is -5/4

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