Question

A line has slope of 7. One of the points on the line is (3,5). Which of the following could be another point on the line? A. (-1,-24)B. (-2,-30)C. (6,24)D. (10,55)

Answer 1

Step-by-step explanation:

The formula for the slope of a line that passes through points (x1, y1) and (x2, y2) is:

`m=(y_1-y_2)/(x_1-x_2)`

We have the slope is 7 and one point is (3, 5). To find which one could be another point we have to replace into the formula each one of the options and see which one satisfies the equality:

A. (-1, -24)

`\begin{gathered} 7=(5-(-24))/(3-(-1)) \\ 7=(5+24)/(3+1) \\ 7=(29)/(4) \\ 7=7.25\text{ }\rightarrow\text{ false} \end{gathered}`

B. (-2, -30)

`\begin{gathered} 7=(5-(-30))/(3-(-2)) \\ 7=(5+30)/(3+2) \\ 7=(35)/(5) \\ 7=7\text{ }\rightarrow\text{ true} \end{gathered}`

C. (6, 24)

`\begin{gathered} 7=(5-24)/(3-6) \\ 7=(-19)/(-3) \\ 7=6.\bar{3}\text{ }\rightarrow\text{ false} \end{gathered}`

D. (10, 55)

`\begin{gathered} 7=(5-55)/(3-10) \\ 7=(-50)/(-7) \\ 7=7.14\text{ }\rightarrow\text{ false} \end{gathered}`

Answer:

B. (-2, -30)