Answer:
Question 9) [tex]y=\frac{-3}{2}x+2 \\\\[/tex]
Question 10) [tex]y=-x-6\\[/tex]
Step-by-step explanation:
Well there are two methods of determining an equation of line
Method 1 (Using the slope-intercept form):
[tex]y=mx+b[/tex]
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):
[tex]y-y_1=m(x-x_1)\\[/tex]
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:
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{-4-2}{4-0} \\\\m=\frac{-6}{4}\\\\m=-3/2 \\[/tex]
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
[tex]y-y_1=m(x-x_1)\\y-2=\frac{-3}{2}(x-0)\\\\y-2=\frac{-3}{2}x\\\\y=\frac{-3}{2}x+2\\\\[/tex]
Question 10)
Two points are (-2 , -4) and (-3 , -3) we use the same method as shown above,
First step calculate the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{-3-(-4)}{-3-(-2)} \\\\m=\frac{-3+4}{-3+2}\\\\m=1/-1\\\\m=-1\\[/tex]
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)
[tex]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\\[/tex]
