Question

I need help. I finished questions 9 and 10. Now I need help with 11 and 12.

Answer 1

Question 9)
`y=(-3)/(2)x+2 \\\\`

Question 10)
`y=-x-6\\`

Explanation:

Well there are two methods of determining an equation of line

Method 1 (Using the slope-intercept form):

`y=mx+b`

This method is mostly used when the y-intercept also known as b is given and the slope also known as m is given

Method 2 (Using the point-slope form):

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

This method is used when a point is given also known as (x1 , y1) and the slope is given which is denoted by m.

Since in Question 9 there is no y-intercept given only two points we will use the second method so here goes,

Q9)

Two points are (0 , 2) and (4 , -4) first step to find out the equation of line is to calculate the slope which is as follows:

`m=(y_2-y_1)/(x_2-x_1) \\\\m=(-4-2)/(4-0) \\\\m=(-6)/(4)\\\\m=-3/2 \\`

Now we have our slope which is m = -3/2 now since we have two points we can use any point in the point-slope form equation because both of these points lie on the line hence satisfying the desired equation that we need so we select the point (0 , 2) [YOU CAN TRY OUT FINDING THE EQUATION OF LINE BY USING THE OTHER POINT THE ANSWERS WOULD BE SAME]

so now we have the point (0 , 2) and value of m = -3/2

`y-y_1=m(x-x_1)\\y-2=(-3)/(2)(x-0)\\\\y-2=(-3)/(2)x\\\\y=(-3)/(2)x+2\\\\`

Question 10)

Two points are (-2 , -4) and (-3 , -3) we use the same method as shown above,

First step calculate the slope:

`m=(y_2-y_1)/(x_2-x_1) \\\\m=(-3-(-4))/(-3-(-2)) \\\\m=(-3+4)/(-3+2)\\\\m=1/-1\\\\m=-1\\`

now we insert the value of m = -1 and take any point of the two points that are given, we select the first point (-2 , -4)

`y-y_1=m(x-x_1)\\y-(-4)=(-1)(x-(-2))\\y+4=(-1)(x+2)\\y+4=-x-2\\y=-x-2-4\\y=-x-6\\`