Question

I don't understand how to do these at all.Ive tried for the last hour. ​

Answer 1

Explanation:

I'll help you out

For #4:

4 Parallel means that the lines have the same slope, but different intercept

I'm going to assume it's 2y - 5x = 10

`2y - 5x = 10\\2y = 5x + 10\\y = (5x)/(2)+5`

the slope is 5/2

We're given that it goes through the point (-10, 9),

we can substitute with the y = mx + b equation

`y = mx + b\\9 = (-10)(5)/2 + b\\9 = -25 + b\\b = 34\\y = (5)/(2)x + 34`

5 Perpendicular means that the slope of the line is the negative reciprocal of the other line

The first line is y = 5, if you look at this on a graph, it's a straight horizontal line. it's slope is 0.

1/0 is undefined, it'd be a straight line upwards, which can be represented by x = (something)

we're given that it goes through (-2, 9)

so the line is

`x = -2`

6

again, parallel = same slope

`m = (y_2-y_1)/(x_2-x_1) \\m = (8-3)/(4-3)\\m = 5\\`

`y = mx + b\\1 = 5(7) + b\\1 = 35 + b\\b = -34\\y = 5x - 34`

7

The two points are (0, 4) and (1, 7)

`m = (7-4)/(1-0)\\ m = 3\\y = mx + b\\-3 = 3(5) + b\\-3 = 15 + b\\b = -18\\y = 3x - 18`

8

the two points are (0, -3) and (3, -1)

`m_1 = (-1 - (-3))/(3-0)\\ m_1 = 2/3\\m_2 = (-3)/(2) \\y = mx + b\\-2 = (-3(2))/(2)+b\\ -2 = -3 + b\\b = 1\\y = (-3)/(2)x+1`

9

This is a straight up line, like in problem 5

it is x = -5

the perpendicular line is a horizontal line y = (something)

since it goes through 3 at -3, it is

`y = 3`

10

the line is y = 4

a parallel line to this is another horizontal line y = (something)

since it goes through 8, the line is

`y = 8`