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write the slope intercept form of the equation of the line through (2,1) and (4,5)

Answer :

Answer:

[tex]y=2x-3[/tex]

Step-by-step explanation:

Hi there!

Slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

1) Determine the slope (m)

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] where the two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (2,1) and (4,5)

[tex]m=\frac{5-1}{4-2}\\m=\frac{4}{2}\\m=2[/tex]

Therefore, the slope of the line is 2. Plug this into [tex]y=mx+b[/tex] :

[tex]y=2x+b[/tex]

2) Determine the y-intercept (b)

[tex]y=2x+b[/tex]

Plug in one of the given points and isolate b

[tex]1=2(2)+b\\1=4+b[/tex]

Subtract both sides by 4

[tex]1-4=4+b-4\\-3=b[/tex]

Therefore, the y-intercept of the line is -3. Plug this into [tex]y=2x+b[/tex]:

[tex]y=2x-3[/tex]

I hope this helps!

Answer:

y=2x-3

Step-by-step explanation:

Slope formula:

[tex]\sf{\dfrac{Y_2-Y_1}{X_2-X_1}[/tex]

y2=5

y1=1

x2=4

x1=2

Solve.

5-1/4-2

Subtract.

5-1=4

4-2=2

Divide.

4/2=2

The slope is 2.

You have to solve with slope-intercept form.

[tex]\sf{y=mx+b}[/tex]

m represents the slope.

b represents the y-intercept.

y-intercept is -3.

[tex]\sf{\boxed{y=2x-3}[/tex]

So, the correct answer is y=2x-3.

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