Respuesta :
For this case we have that by definition, the equation of the line in slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cutoff point with the y axis
We have:
[tex](x1, y1): (- 8,11)\\(x2, y2): (4,3.5)[/tex]
[tex]m = \frac {y2-y1} {x2-x1} = \frac {3.5-11} {4 - (- 8)} = \frac {-7.5} {4 + 8} = \frac {-7.5} {12 } = - \frac {\frac {15} {2}} {12} = - \frac {15} {24} = - \frac {5} {8}[/tex]
Thus, the equation will be given by:
[tex]y = - \frac {5} {8} x + b[/tex]
We substitute a point to find "b":
[tex]11 = - \frac {5} {8} (- 8) + b\\11 = 5 + b\\b = 11-5\\b = 6[/tex]
Finally:
[tex]y = - \frac {5} {8} x + 6[/tex]
Answer:
[tex]y = - \frac {5} {8} x + 6[/tex]
Answer:
So our answers could be any of these depending on the form wanted*:
[tex]y=\frac{-5}{8}x+6[/tex]
[tex]5x+8y=48[/tex]
[tex]y-11=\frac{-5}{8}(x+8)[/tex]
[tex]y-\frac{7}{2}=\frac{-5}{8}(x-4)[/tex]
*There are other ways to write this equation.
Step-by-step explanation:
So we are given two points on a line: (-8,11) and (4,7/2).
We can find the slope by using the formula [tex]\frac{y_2-y_1}{x_2-x_1} \text{ where } (x_1,y_1) \text{ and } (x_2,y+2) \text{ is on the line}[/tex].
So to do this, I'm going to line up my points vertically and then subtract vertically, then put 2nd difference over 1st difference:
( 4 , 7/2)
-(-8 , 11)
----------------
12 -7.5
So the slope is -7.5/12 or -0.625 (If you type -7.5 division sign 12 in your calculator).
-0.625 as a fraction is -5/8 (just use the f<->d button to have your calculator convert your decimal to a fraction).
Anyways the equation of a line in slope-intercept form is y=mx+b where m is the slope and b is y-intercept.
We have m=-5/8 since that is the slope.
So plugging this into y=mx+b gives us y=(-5/8)x+b.
So now we need to find b. Pick one of the points given to you (just one).
Plug it into y=(-5/8)x+b and solve for b.
y=(-5/8)x +b with (-8,11)
11=(-5/8)(-8)+b
11=5+b
11-5=b
6=b
So the equation of the line in slope-intercept form is y=(-5/8)x+6.
We can also put in standard form which is ax+by=c where a,b,c are integers.
y=(-5/8)x+6
First step: We want to get rid of the fraction by multiplying both sides by 8:
8y=-5x+48
Second step: Add 5x on both sides:
5x+8y=48 (This is standard form.)
Now you can also out the line point-slope form, [tex]y-y_1=m(x-x_1) \text{ where } m \text{ is the slope and } (x_1,y_1) \text{ is a point on the line }[/tex]
So you can say either is correct:
[tex]y-11=\frac{-5}{8}(x-(-8))[/tex]
or after simplifying:
[tex]y-11=\frac{-5}{8}(x+8)[/tex]
Someone might have decided to use the other point; that is fine:
[tex]y-\frac{7}{2}=\frac{-5}{8}(x-4)[/tex]
So our answers could be any of these depending on the form wanted*:
[tex]y=\frac{-5}{8}x+6[/tex]
[tex]5x+8y=48[/tex]
[tex]y-11=\frac{-5}{8}(x+8)[/tex]
[tex]y-\frac{7}{2}=\frac{-5}{8}(x-4)[/tex]
