Question

(-5,7), (4,-8)

Those above are your two points. Find the slope and y-intercept using the equation

y=mx+b,

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Answer 1

Given:

Two points- (-5,7) and (4,-8)

To Find:

Slope and y-intercept of line passing through given points using the equation

y=mx+b

Solution:

We know that,

• Equation of a line passing through two points (x₁,y₁) and (x₂,y₂) is given by

$\longrightarrow\bf{y-y_{1}=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1})}$

• Equation of a straight line can be written as

$\longrightarrow\bf{y=mx+c}$

where

• m is the slope of the given line
• c is a constant and y-intercept of given line

Now, here

• x₁= -5
• x₂= 4
• y₁= 7
• y₂= -8

So, equation of line passing through given points is

$\longrightarrow\mathrm{y-7=\dfrac{-8-7}{4-(-5)}(x-(-5))}$

$\longrightarrow\mathrm{y-7=\dfrac{-15}{4+5}(x+5)}$

$\longrightarrow\mathrm{y-7=\dfrac{\cancel{-15}}{\cancel{9}}(x+5)}$

$\longrightarrow\mathrm{y-7=\dfrac{-5}{3}(x+5)}$

$\longrightarrow\mathrm{3(y-7)=-5(x+5)}$

$\longrightarrow\mathrm{3y-21=-5x-25}$

$\longrightarrow\mathrm{3y=-5x-25+21}$

$\longrightarrow\mathrm{3y=-5x-4}$

$\longrightarrow\mathrm{y=\dfrac{-5x-4}{3}}$

$\longrightarrow\mathrm{y=\dfrac{-5x}{3}-\dfrac{4}{3}}$

$\longrightarrow\mathrm{y=\bigg(\dfrac{-5}{3}\bigg)x+\bigg(-\dfrac{4}{3}\bigg)}---(1)$

And we know that an equation of straight line can be expressed as

y= mx+b------------------(2)

On comparing (1) and (2), we get

$\mathrm{\pink{Slope=m=\dfrac{-5}{3}}}$

$\mathrm{\green{y-intercept=b=\dfrac{-4}{3}}}$

Hence, slope of line passing through given points is -5/3 and y-intercept of given line is -4/3.

Answer 2

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