Question

The point-slope form of the equation of the line that passes through (-9, -2) and (1, 3) is y-

- 1). What is the slope
intercept form of the equation for this line?
y= {x+2
y=2x-4
0 = 2 x + 3

Answer 1

`\huge\boxed{y=(1)/(2)x+(5)/(2)}`

Explanation:

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

We have two points (-9, -2) and (1, 3).

Substitute:

`m=(3-(-2))/(1-(-9))=(5)/(10)=(1)/(2)`

The point-slope form of an equation of a line:

`y-y_1=m(x-x_1)`

For (-9, -2):

`y-(-2)=(1)/(2)(x-(-9))\\\\y+2=(1)/(2)(x+9)`

For (1, 3):

`y-3=(1)/(2)(x-1)`

The slope-intercept form of an equation of a line:

`y=mx+b`

b - y-intercept

Put the coordinates of the point (1, 3) and the value of a slope to the equation of a line:

`3=(1)/(2)\cdot1+b\\\\3=(1)/(2)+b\qquad\text{subtract}\ \dfraC{1}{2}\ \text{from both sides}\\\\2(1)/(2)=b\to b=(5)/(2)`

The equation of a line in the slope-intercept form is:

`y=(1)/(2)x+(5)/(2)`