Respuesta :
Answer:
1) The slope for the given points (6,7) and (-10,4) is [tex]m=\frac{3}{16}[/tex]
2) The slope for the given points (17,4) and (13,20) is [tex]m=-4[/tex]
3) The slope for the given points (12,19) and (14,18) is [tex]m=-\frac{1}{2}[/tex]
4) The slope for the given points (-11,0) and (18,13) is [tex]m=\frac{13}{29}[/tex]
5) The slope for the given points (3,6) and (-8,20) is [tex]m=-\frac{14}{11}[/tex]
6) The slope for the given points (-16,-20) and (12,5) is [tex]m=\frac{25}{28}[/tex]
7) The slope for the given points (13,20) and (14,-14) is [tex]m=-34[/tex]
8) The slope for the given points (18,15) and (3,0) is [tex]m=1[/tex]
Step-by-step explanation:
To find the slope of the line through each pair of points:
1) Given points are (6,7) and (-10,4)
The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (6,7) and (-10,4) respectively
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{4-7}{-10-6}[/tex]
[tex]m=\frac{-3}{-16}[/tex]
[tex]m=\frac{3}{16}[/tex]
Therefore the slope for the given points (6,7) and (-10,4) is [tex]m=\frac{3}{16}[/tex]
2) Given points are (17,4) and (13,20)
The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (17,4) and (13,20) respectively
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{20-4}{13-17}[/tex]
[tex]m=\frac{16}{-4}[/tex]
[tex]m=-4[/tex]
Therefore the slope for the given points (17,4) and (13,20) is [tex]m=-4[/tex]
3) Given points are (12,19) and (14,18)
The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (12,19) and (14,18) respectively
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{18-19}{14-12}[/tex]
[tex]m=\frac{-1}{2}[/tex]
Therefore the slope for the given points (12,19) and (14,18) is [tex]m=-\frac{1}{2}[/tex]
4) Given points are (-11,0) and (18,13)
The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (-11,0) and (18,13) respectively
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{13-0}{18-(-11)}[/tex]
[tex]m=\frac{13}{29}[/tex]
Therefore the slope for the given points (-11,0) and (18,13) is [tex]m=\frac{13}{29}[/tex]
5) Given points are (3,6) and (-8,20)
The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (3,6) and (-8,20) respectively
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{20-6}{-8-3}[/tex]
[tex]m=\frac{14}{-11}[/tex]
[tex]m=-\frac{14}{11}[/tex]
Therefore the slope for the given points (3,6) and (-8,20) is [tex]m=-\frac{14}{11}[/tex]
6) Given points are (-16,-20) and (12,5)
The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (-16,-20) and (12,5) respectively
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{5-(-20)}{12-(-16)}[/tex]
[tex]m=\frac{5+20}{12+16}[/tex]
[tex]m=\frac{25}{28}[/tex]
Therefore the slope for the given points (-16,-20) and (12,5) is [tex]m=frac{25}{28}[/tex]
7) Given points are (13,20) and (14,-14)
The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (13,20) and (14,-14) respectively
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{-14-20)}{14-13}[/tex]
[tex]m=\frac{-34}{1}[/tex]
[tex]m=-34[/tex]
Therefore the slope for the given points (13,20) and (14,-14) is [tex]m=-34[/tex]
8) Given points are (18,15) and (3,0)
The slope formula is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Let [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] be the given points (18,15) and (3,0) respectively
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m=\frac{0-15}{3-18}[/tex]
[tex]m=\frac{-15}{-15}[/tex]
[tex]m=1[/tex]
Therefore the slope for the given points (18,15) and (3,0) is [tex]m=1[/tex]
