Question

Write the equation of the line in fully simplified slope-intercept form.

Answer 1

Answer: y=2x-5

Explanation:

Choose two points on the graph: (0,-5) and (3,1)

The straight line equation is: y=mx+b

1)

`\displaystyle\\\boxed {The\ slope\ m\ =(y_2-y_1)/(x_2-x_1) }`

`\displaystyle\\x_1=0\ \ \ \ \ x_2=3 \ \ \ \ y_1=-5\ \ \ \ y_2=1\\\\ Hence,\\\\m=(1-(-5))/(3-0) \\\\m=(1+5)/(3) \\\\m=(6)/(3) \\\\m=2\\\\Thus,\ y=2x+b\ \ \ \ \ (1)`

2)

To determine the coefficient b, take any of the two points,

for example, (0,-5), that is, x=0 y=5

Substitute these values into formula (1):

`-5=2*0+b\\-5=0+b\\-5=b\\Thus,\ b=-5`

The result is y=2x-5

Answer 2

Explanation:

a slope-intercept form :

y = ax + b

"a" is the slope, "b" is the y-intercept (the y-value when x = 0).

the slope is the ratio (y coordinate change / x coordinate change) when moving from on point on the line to another.

"b" we can read off the graph : when x = 0, then y = -5.

so, b = -5.

for the slope let's pick 2 points. your teacher has kindly marked already points with integer coordinates.

so, I pick (3, 1) and (4, 3).

x changes by +1 (from 3 to 4).

y changes by +2 (from 1 to 3).

so, the slope is

+2/+1 = 2/1 = 2

the equation is

y = 2x - 5