Question

What equation in slope intercept form represents the line that passes through the points (2, 1) and (5, -8)?

Answer 1

Step-by-step explanation:

y-1=(-3)(x-2) is the ans

Answer 2

Given :-

➛ The points on the line are (2,1) and (5,-8)

To Find :-

➛ Slope of the line

➛ Equation in slope intercept form ⠀⠀represents the line passes through the ⠀⠀points (2, 1) and (5, -8)

Solution :-

➙ To Write an equation in slope intercept form we always need a points and a slope, Here isn't given a slope but two points are given So, we can find slope from those points

➯ Let the first point (2, 1) be ( x1 , y1 )

➯ And, the second point (5, -8) be ( x2 , y2 )

As we know that,

⠀⠀⠀$★ {\red{\boxed{\large{\bold{m = \frac{ y_{2}- y_{1} }{ x_{2}- x_{1} } }}}}} ★$

where,

• m = Slope of a line

• x2 and y2 = ( 5, -8 )

• x1 and y1 = ( 2, 1 )

By substituting values we get,

$\begin{gathered} \implies\bf \frac{ - 8 - 1}{ 5 - 2} \\ \end{gathered}$

$\begin{gathered}\implies\bf \cancel{\frac{ - 9}{3} } \\ \end{gathered}$

$\begin{gathered} \implies\bf - 3\\ \end{gathered}$

∴ Slope of a line is -3

______________________

➙ Now, we will use point-slope formula to find an equation of the line using slope and first point ( you can also use 2nd point instead if you prefer)

Point-Slope formula :

⠀⠀⠀$★ {\red{\boxed{\large{\bold{y - y_{1} = m(x - x_{1})}}}}} ★$

Where,

• x1 and y1 = (2, 1)

• m = Slope of a line ( -3 )

By substituting values according to the formula we get,

$\begin{gathered}\implies\bf y - 1 = - 3(x - 2) \\ \end{gathered}$

$\begin{gathered}\implies\bf y - 1 = - 3x + 6 \\ \end{gathered}$

$\begin{gathered}\implies\bf y = - 3x + 6 + 1\\ \end{gathered}$

$\begin{gathered}\implies \large{\bf {\red {\: y = - 3x + 7} }} \\ \end{gathered}$

${\underline{\boxed{\small{\bf{\therefore The\: equation \: is \: (y = - 3x + 7) }}}}}$