What is the y-intercept and slope of this table?

Question

X. Y

10. 43

-2. -5

6. 27

Answer 1

Hello, Pearl,

Let's look at the points in ascednding order of x:

X Y

-2 -5

6 27

10 43

Take the first two points and calculate the slope of the line connecting them:

Y: (27 - (-5)) , = 32

X: (6 - (-2) = 8

Slope = 32/8 or 4

The slope between the first and last points is also 4:

Y: (43 - (-5)) = 48

X: (10 - (-2)) = 12

Slope = 48/12, or 4

The slope is the same between all points so we can predict a straight line of the form y = mx + b. m is the slope, 4 in this case.

y = 4x + b

Use one of the points to find b, the y-intercept:

-5 = 4(-2) + b

b = 3

3 is the y-intercept. The line crosses the y axis at 3 when x is 0.

The line that intersects all points is y = 4x + 3

Try some of the points to confirm this.

43 = 4*(10) + 3? Yes

Bob

Answer 2

All it takes is two points to define a line. Let's pick (10,43) and (6,27). The equation of a line is:

y = mx + b

where m is the slope and b is the y-intercept. The formula for the slope is:

m = (y₂-y₁)/(x₂-x₁) = (27-43) / (6-10) = (-16)/(-4) = 4

So our equation so far is:

y = 4x + b

To find b, plug in any the given points. Let's use (-2, -5):

y = 4x + b

-5 = 4(-2) + b

-5 = -8 + b

3 = b

y = 4x + 3