Question

Find the slope of the line that passes through (3,10) and (1,17)​

Answer 1

slope = -
`(7)/(2)`

Explanation:

calculate the slope m using the slope formula

m =
`(x_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (3, 10 ) and (x₂, y₂ ) = (1, 17 )

m =
`(17-10)/(1-3)` =
`(7)/(-2)` = -
`(7)/(2)`

Answer 2

`m=- (7)/(2)`

Explanation:

The slope of a line passing through the two points
`\displaystyle{\large{{P}={\left({x}_{{1}},{y}_{{1}}\right)}}}` and
`\displaystyle{\large{{Q}={\left({x}_{{2}},{y}_{{2}}\right)}}}` is given by
`\displaystyle{\large{{m}=\frac{{{y}_{{2}}-{y}_{{1}}}}{{{x}_{{2}}-{x}_{{1}}}}}}`.

We have that
`x_1=3`,
`y_1=10`,
`x_2=1`,
`y_2=17`.

Plug the given values into the formula for slope:
`m=(\left(17\right)-\left(10\right))/(\left(1\right)-\left(3\right))=(7)/(-2)=- (7)/(2)`

Answer: the slope of the line is
`m=- (7)/(2)`.