Find the linear equation in slope intercept form that passes through the points (5,3) and (2,-1)

[tex]\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-3}{2-5}\implies \cfrac{-4}{-3}\implies \cfrac{4}{3} \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-3=\cfrac{4}{3}(x-5)\implies y-3=\cfrac{4}{3}x-\cfrac{20}{3} \\\\\\ y=\cfrac{4}{3}x-\cfrac{20}{3}+3\implies y=\cfrac{4}{3}x-\cfrac{11}{3}[/tex]

First, we must determine the slope:

Slope = m = (Y2 -Y1) ÷ (X2 -X1)

Slope = (-1, -3) / (2 -5)

Slope = -4 / -3 = 4 / 3 = 1.33333333...

Now, we have to fill in this equaton:

y = mx + b we know the slope "m"

y = 1.3333... x + b now we'll take a point (5, 3) and solve for "b"

b = y -mx b = 3 - 1.3333... *5

b = -3.6666666667

y = 1.3333... x -3.6666...

Source

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[tex]\bf (\stackrel{x_1}{-8}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{4}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-8)}}}\implies \cfrac{-9}{1+8}\implies \cfrac{-9}{9}\implies -1[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{-1}[x-\stackrel{x_1}{(-8)}]\implies y-4=-(x+8) \\\\\\ y-4=-x-8\implies y=-x-4[/tex]

A linear equation in slope intercept form that passes through the points (-11 -5) and (1 -2) is:

[tex]y=\frac{1}{4}x-\frac{9}{4}[/tex]

Step-by-step explanation:

Given points are:

(-11, -5) = (x1,y1)

(1, -2) = (x2,y2)

We have to find the slope first

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{-2-(-5)}{1-(-11)}\\m=\frac{-2+5}{12}\\m=\frac{3}{12}\\m=\frac{1}{4}[/tex]

Slope-intercept form is:

[tex]y=mx+b[/tex]

Put the value of slope

[tex]y=\frac{1}{4}x+b[/tex]

To find the value of b, putting the point (1 -2) in equation

[tex]-2=\frac{1}{4}(1)+b\\-2=\frac{1}{4}+b\\-2-\frac{1}{4}=b\\b=\frac{-8-1}{4} \\b=\frac{-9}{4}[/tex]

Putting the values of b and m

[tex]y=\frac{1}{4}x-\frac{9}{4}[/tex]

A linear equation in slope intercept form that passes through the points (-11 -5) and (1 -2) is:

[tex]y=\frac{1}{4}x-\frac{9}{4}[/tex]

Keywords: Equation of line, slope-intercept form

Learn more about equation of line at:

#LearnwithBrainly

The linear equation in slope intercept that passes through given points as  y = [tex]\frac{1}{4}[/tex] x - [tex]\frac{9}{4}[/tex]  .

Step-by-step explanation:

Given points for the line equation as

( - 11 , - 5 )  and  ( 1 , - 2 )

The equation of line in slope intercept form as

[tex]y - y_1 = m ( x - x_1)[/tex]

where m is the slope of the line

So , slope can be calculated as

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Or, m =  [tex]\frac{ - 2 + 5 }{1 + 11}[/tex]

Or, m =   [tex]\frac{ 3 }{12}[/tex]

∴   m =  [tex]\frac{ 1 }{4}[/tex]

Now The equation of line with slope  [tex]\frac{ 1 }{4}[/tex]  and points is

[tex]y - y_1 = m ( x - x_1)[/tex]

Or, [tex]y+5 = \frac{1}{4} (x + 11)[/tex]

Or, 4 y + 20 = x + 11

Or, 4 y = x + 11 - 20

∴   4 y = x - 9

I,e  y = [tex]\frac{1}{4}[/tex] x - [tex]\frac{9}{4}[/tex]  

Hence The linear equation in slope intercept that passes through given points as  y = [tex]\frac{1}{4}[/tex] x - [tex]\frac{9}{4}[/tex]  .  Answer

y=4/5x-4

Step-by-step explanation:

Use point-slope formula then turn to slope intercept form

y-y₁=m(x-x₁)  →   y = mx + b

y--8=4/5(x--5)

y+8=4/5x+4

  -8             -8

y=4/5x-4

y=4x+9

Step-by-step explanation:

from -11 to 1 is 12 units and from -5 to -2 is 3

slope 12/3 can be simplified to 4/1 or 4

now we have y=mx y=4x now we need b

to get to the y intercept i looked at 1,-2 and used the slope 2 times making the int. 9

Equation is y=mx+b so solve for m with the equation m=y2-y1/x2-x1. so m= -1-7/-2-4. m=4/3.
y=4/3x+7

X<5-6+(-10+3)/×>-7-(-5-1)