Find the equation of the linear function k going through (-16,14), (6,15)

Answer 1

Find the equation of the linear function k going through (-16,14), (6,15)

Y = MX + B is the EQUATION of a straight line.

M = the SLOPE of the line. The RISE divided by the RUN.

B = the Y-INTERCEPT. Where the line crosses the Y AXIS, and X = 0.

First, find the SLOPE:

M = (15 - 14)/(6 - (-16))

= 1/(6 + 16)

= 1/22

Second, find the Y-INTERCEPT B using either of the two points on the line.

Let's use (6,15).

Plug in 6 for X, 15 for Y, and 1/22 for M into our SLOPE-INTERCEPT EQUATION.

Y = MX + B

15 = (1/22)(6) + B

15 = 3/11 + B

14 8/11 = B Subtracting 3/11 from both sides.

ANSWER: Y = (1/22)X + 14 8/11

CHECKING:

DOES (6,15) LIE ON THIS LINE?

Does 15 = (1/22)(6) + 14 8/11

(1/22)(6) + 14 8/11 = (6/22) + 14 8/11 = 3/11 + 14 8/11 = 14 + 11/11 = 14 + 1 = 15 Yes!

DOES (-16,14) LIE ON THIS LINE?

Does 14 = (1/22)(-16) + 14 8/11

(1/22)(-16) + 14 8/11

= (-16/22) + 14 8/11

= (-8/11) + 14 8/11

= 14 Yes!

Hope this helps you Jordyn.

Answer 2

Hi Jordyn,

You can write the equation of a line in the slope -intercept form here: y = mx + b where m is the slope and b is the y-intercept.

Use the two points to determine the slope:

m = (y₂ - y₁ ) = (14 - 15) = -1 = 1

(x₂ - x₁) ( -16 - 6) -22 22

Use either point to determine the y-intercept by substituting the x and y coordinates and the calculated slope into the slope-intercept form and solving for b. Let's try (6,15):

y = mx + b

15 = 1 • 6 + b

22

15 = 3 + b

11

14 8 = b

11

The equation of the line will be:

y = 1 x + 14 8

22 11