Find an equation for the line that passes through the points , −1−6 and , 5−2

The equation is

y = 2x/3 + 4/3

Step-by-step explanation:

The equation of a straight line is represented in the slope-intercept form, y = mx + c

Where c = y intercept

Slope, m = change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

From the information given,

The points through which the line passed through are −1, −6 and , 5, −2

Slope, m = (y2-y1)/(x2-x1)

y2 = -2

y1 = -6

x2= 5

x1 = -1

Slope, m = (-2- -6)/(5- -1)

= 4/6 = 2/3

To find intercept, c

Let's use ( 5, −2)

-2 = 2/3 ×5 + c

-2 = 10/3 + c

c = -2 + 10/3 = 4/3

The slope-intercept equation will be

y = 2x/3 + 4/3

sss (side, side, side)

sas (side, angle, side)

asa (angle, side, angle)

aas (angle, angle, side)

hl (hypotenuse, leg)