Respuesta :
Step-by-step explanation:
Point slope-form of a line passing through the point [tex](x_0, y_0)[/tex] and having m is [tex]y-y_0=m(x-x_0)\cdots(i)[/tex]
The slope-intercept form of a line having slope m and y-intercept c is
[tex]y=mx+c\cdots(ii)[/tex]
(1). The line is passing through [tex](x_0, y_0)=(-5,6)[/tex] and having the slope m=3.
So, by using equation (i), the point-slope form of the line is
[tex]y-6=3(x-(-5))[/tex]
[tex]\Rightarrow y-6=3(x+5)[/tex]
By using equation (ii), the slope-intercept form of the line is
[tex]y=3x+c\cdots(iii)[/tex]
as the line is passing through the point (-5,6), so pout this point in the equation (iii) to get the value of c.
[tex]6=3\times(-5)+c[/tex]
[tex]\Rightarrow 6=-15+c[/tex]
[tex]\Rightarrow c=6+15=21[/tex]
From equation (iii), the slope-intercept form of the line is [tex]y=3x+21[/tex].
(2). The line is passing through the points (–5, 9) and (1, 3).
As two points are given, so the slope of the line is
[tex]m=\frac{3-9}{1-(-5)}=-1.[/tex]
Now, proceeding in the same way as in part (1),
By using equation (i), the point-slope form of the line is
[tex]y-3=-1(x-1)[/tex] [taking point (1,3) and m=-1]
By using equation (ii), the slope-intercept form of the line is
[tex]y=(-1)x+c\cdots(iv)[/tex]
as the line is passing through the point (1,3), so pout this point in the equation (iv) to get the value of c.
[tex]3=-1\times1+c[/tex]
[tex]\Rightarrow 3=-1+c[/tex]
[tex]\Rightarrow c=3+1=4[/tex]
From equation (iv), the slope-intercept form of the line is y=-x+4.
