430,884 views
28 votes
28 votes
Write the equation of each line below in slope intercept form. 3. Parallel to y = 6x - 3 and passes through (1,7). 4. Perpendicular to y = 5 x + 1 and passes through (3,-2). 5. Perpendicular to 3x + 2y = 8 and passes through (9,4). I6. perpendicular to y=3/5x+1 and passes through ( 3,-2)

User Theiaz
by
2.8k points

1 Answer

12 votes
12 votes

Slope-intercept form:

y = mx + b

where m is the slope and b the y-intercept

3. if two lines are parallel, then they have the same slope. In

y = 6x - 3

the slope is 6, then m = 6

If the line passes through (1,7), then it satisfies the next equation:

7 = 6*1 + b

7 - 6 = b

1 = b

Then, the equation is: y = 6x + 1

4. If two lines are perpendicular then the multiplication of their slopes is equal to -1. In y = 5x + 1, the slope is 5, then:

5*m = -1

m = -1/5

The line passes through (3,-2), that is, when x = 3, y = -2. Replacing these values into the general equation, we get:

y = mx + b

-2 = (-1/5)*3 + b

-2 = -3/5 + b

-2 + 3/5 = b

-1.4 = b

Then, the equation is: y = -1/5x - 1.4

5. To get the slope of 3x + 2y = 8 , we have to isolate y, as follows:

3x + 2y = 8

2y = 8 - 3x

y = (8 - 3x)/2

y = 8/2 - 3/2x

y = 4 - 3/2x

so, its slope is -3/2

The slope of the new line is:

m*(-3/2) = -1

m = (-1)*(-2/3)

m = 2/3

The line passes through (9,4), that is, when x = 9, y = 4. Replacing these values into the general equation, we get:

y = mx + b

4 = 2/3*9 + b

4 = 6 + b

4 - 6 = b

-2 = b

Then, the equation is: y = 2/3x - 2

6. In y = 3/5x + 1, the slop is 3/5. Then, the slope of the new line is:

m*3/5 = -1

m = (-1)*5/3

m = -5/3

The line passes through ( 3,-2), then:

-2 = (-5/3)*3 + b

-2 = -5 + b

-2 + 5 = b

3 = b

Then, the equation is: y = -5/3x + 3

User Vineel Shah
by
2.7k points