Writing equations of Linear Functions

Question

Writing equations of linear functions, please help! 

The chart below is asking what the slope, y intercept, and equations are. 

In the first chart it has x on the left and underneath are the numbers: 1,2,3,4 and 5

And on the right is y with the numbers 1.7, 1.1, 0.5, -0.1 and -0.7 

How would I identify the slope, y intercept, and equation for this problem?

Answer 1

You can suppose:

x1=1, x2=2, x3=3, x4=4, x5=5

y1=1.7, y2=1.1, y3=0.5, y4= -0.1, y5= -0.7

As we know: slope = m = (y2 - y1) / (x2 - x1) → m = (1.1-1.7) / (2 - 1) = - 0.6

We can also use other pairs of x and y to find slope:

For example: m = (y4 - y2) / (x4 - x2) → m = (- 0.1 - 1.1) / (4 - 2 ) = (-1.2) / 2 = - 0.6

Line equation when we know its slope and a point is:

y - y1 = m (x - x1) → y - 1.7 = (-0.6) (x - 1) → y = (-0.6) (x - 1) + 1.7 → y = - 0.6 x + 2.3

We can also use other points to find line equation:

y - y3 = m (x - x3) → y - 0.5 = (-0.6) (x - 3) → y = (-0.6) (x - 3) + 0.5 → y = - 0.6 x + 2.3

We can find y intercept when x=0:

y = - 0.6 (0) + 2.3 → y = 2.3

All of pairs (x,y) satisfy the line equation (y = - 0.6 x + 2.3)

For example (4, - 0.1) → y = - 0.6 (4) + 2.3 → y = - 0.1

Answer 2

You have a sequence of data that shows how the y value changes as you increase the x value in steps of 1.

From x=1 to x=2, the y-value decreases by 0.6. So the slope of this line would be -0.6 (negative because it is decreasing). You can check this is true between any two pairs of values.

The y-intercept is the value at x=0. So this will be 0.6 higher than it is at x=1. Hence y-intercept is 2.3

The equation therefore would be y=-0.6x+2.3

Answer 3

m (slope) = Δy (change in y) / Δx (change in x)

For each change of 1 in x y changes by - 0.6

The slope is -0.6 / 1

y = mx + b slope-intercept form

y = -0.6x + b

1.7 = -0.6(1) + b

2.3 = b

y- intercept is (0, 2.3)

y = -0.6x + 2.3