Considering the expression of a line, you obtain:
(a) the equation of the line that passes through the pair of points (1,7) and (4,22) is y=5x + 2.
(b) the equation of the line that passes through the pair of points (-2,13) and (2,3) is y=-2.5x + 8.
(c) the equation of the line that passes through the pair of points (4,6) and (10,0) is y=-1x + 10.
(d) the equation of the line that passes through the pair of points (0, -10) and (16, 2) is y= 0.75x - 10.
A linear equation o line can be expressed in the form y = mx + b.
where
Knowing two points (x1, y1) and (x2, y2) of a line, the slope m of said line can be calculated using the following expression:
[tex]m=\frac{y2 -y1}{x2 -x1}[/tex]
Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.
So, in this case, you can calculated in this case:
(a) Being (x1,y1)= (1,7) and (x2,y2)= (4,22), the slope m can be calculated as:
[tex]m=\frac{22 -7}{4 -1}[/tex]
m= 5
Considering point 1 and the slope m, you obtain:
7= 5×1 + b
7= 5 +b
7-5= b
2=b
Finally, the equation of the line that passes through the pair of points (1,7) and (4,22) is y=5x + 2.
(b) Being (x1,y1)= (-2,13) and (x2,y2)= (2,3), the slope m can be calculated as:
[tex]m=\frac{3 -13}{2 -(-2)}[/tex]
m= -2.5
Considering point 2 and the slope m, you obtain:
3= -2.5×2 + b
3= -5 +b
3+5= b
8=b
Finally, the equation of the line that passes through the pair of points (-2,13) and (2,3) is y=-2.5x + 8.
(c) Being (x1,y1)= (4,6) and (x2,y2)= (10,0) , the slope m can be calculated as:
[tex]m=\frac{0 -6}{10 -4}[/tex]
m= -1
Considering point 1 and the slope m, you obtain:
6= -1×4 + b
6= -4 +b
6+4= b
10=b
Finally, the equation of the line that passes through the pair of points (4,6) and (10,0) is y=-1x + 10.
(d) Being (x1,y1)= (0,-10) and (x2,y2)= (16,2) , the slope m can be calculated as:
[tex]m=\frac{2 -(-10)}{16 -0}[/tex]
m= 0.75
Considering point 2 and the slope m, you obtain:
2= 0.75×16 + b
2= 12 +b
2-12= b
-10=b
Finally, the equation of the line that passes through the pair of points (4,6) and (10,0) is y= 0.75x - 10.
Learn more about the equation of a line having 2 points:
