Question

Help on the ones you know

Answer 1

2. y = x + 13

Explanation:

Your points are: (-4, 9) and (2, 15)

To write an equation of a line from two ordered pairs, you first find the slope (m)

To find the slope, you do y2 - y1 / x2 - x1

(-4 is x1, 9 is y1) (2 is x2, 15 is y2)

Plug in the numbers:

15 - 9 / 2 - (-4) ----------------------> 6/6 ----------> 1, m = 1

The next equation we'll use is y - y1 = m(x - x1)

and slope intercept form is y = mx + b

Pick either ordered pair to plug in the coordinates, but this time I'll use

(2, 15) -----> 2 is x1, 15 is y1

y - 15 = m(x - 2)

Since we already know the slope, m, we can simplify the equation.

y - 15 = 1(x - 2)

Distributive property

y - 15 = x - 2

Add 15 on both sides,

y = x + 13

Answer 2

1. y=(2/3)x-4
slope is rise/run. starting at (0,-4), i counted up 4 to the x-axis then over 6 to the point (6,0). this gives a slope of 4/6, which is then reduced to 2/3. our b in the y=mx+b is found by looking for where the line crosses the y-axis, which is at (0,-4). b is this y value. plugging everything in (m for slope, b for y-intercept) gives y=(2/3)x-4

2. the other commenter did a great job at explaining 2

3. the line with a slope of -3 is steeper
start this problem by solving for y in the equation given. -5x+2y=8 becomes 2y=5x+8, then y=(5/2)x+4. all we need from this is the slope 5/2 to compare to -3. a steeper slope is given by the larger absolute value. |5/2| is 5/2, and |-3| is 3. 5/2<3, so the line with the slope -3 is steeper.

4a. the lines are neither perpendicular or parallel.
the slopes are different, so they cannot be parallel. the slope of the first equation and second equation (-4 and 4) are not inverse reciprocals of each other, so they cannot be perpendicular.

4b. the lines are parallel.
to find the answer of this question, solve for y in the first equation. 5x+15y=-8 becomes 15y=-5x-8, then y=-(1/3)x-(8/15). the slopes of the lines are both -1/3 with different y-intercepts, so the lines are parallel.

5. y=(1/3)x-(14/3)
use point-slope form and simplify. plugging into point slope gives us y+2=m(x-8). m is found by taking the inverse reciprocal of the equation given to us. the inverse reciprocal of -3 is 1/3, so m=1/3. the equation is y+2=(1/3)(x-8). distribute to get y+2=(1/3)x-(8/3). solve for y. y=(1/3)x-(8/3)-2. y=(1/3)x-(8/3)-(6/3). y=(1/3)x-(14/3)