Respuesta :
a) x – 2y + 6 = 0 b) x + y = 1 c) y = 1 d) y = -3x + 8
Solution:
a. The points (-4,1) and (2,4) both lie on the line
The general line equation on which (a, b) and (c, d) lies is:
[tex]y-\mathrm{b}=\frac{d-b}{c-a}(x - a)[/tex]
Here the given points are (a, b) = (-4, 1) and (c, d) = (2, 4)
Thus the required equation is:
[tex]y-1=\frac{4-1}{2-(-4)}(x-(-4))[/tex]
On solving we get,
[tex]\begin{array}{l}{\rightarrow y-1=\frac{3}{2+4}(x+4)} \\\\ {\rightarrow y-1=\frac{3}{6}(x+4)} \\\\ {\rightarrow 2(y-1)=1(x+4)} \\\\ {\rightarrow 2 y-2=x+4} \\\\ {\rightarrow x-2 y+6=0}\end{array}[/tex]
b.) m= -1 and the point (2, -1) lies on the line
The equation of line in point slope form is y – b = m(x – a)
where m is slope and (a, b) is a point on it
Here m = -1 and (a, b) = (2, -1)
Thus the required equation is:
y – (-1) = -1(x - 2)
y + 1 = -x + 2
y = -x + 2 -1
y = -x + 1
c. )It has the same slope as y = 5 and passes through (1, 1)
our line has same slope with y = 5, then our equation would be y = k and it passes through (x, y) = (1, 1) so, then by substitution
1 = k
k =1
Then our equation will be y = k
y = 1
d. ) m= -3 and it has a y-intercept of (0, 8)
line equation in slope intercept form is y = mx + b where m is slope and b is y – intercept.
Then, our equation will be y = -3x + 8
We took y- intercept = 8 as it is the value of y when x = 0
