Help with writing linear equations

Question

Question 1: Write an equation in slope intercept form of the line through (4,2) with the slope of 1/2.

 

Question 2: Write an equation in Point slope form for the line that passes through (2,-5) and (6,3). Then write the equation in slope intercept form. 

 

Question 3: Find the slope intercept form of the equation of the line that passes through (-5,3) and is parallel to 12x - 3y =10

Answer 1

1) use point-slope formula

 

y - 2 =1/2(x-4)

 

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

 

y = 1/2(x)

 

2) find the slope first

 

m = (3 - - 5)/(6-2)

 

m = 8/4 = 2

 

now point-slope

 

y-3 =2(x-6)

 

3) the slope of the line given is found by solving for y

 

-3y = -12x + 10

 

y = 4x - 10/3

 

slope = 4

 

The line we need will also have a slope of 4 because it's parallel

 

use point-slope initially

 

y-3 = 4(x - -5)

 

y-3 =4x+ 20

 

y = 4x + 23