Respuesta :

texaschic101
(2,-4)(6,10)
slope(m) = (10 - (-4) / (6 - 2) = (10 + 4) / 4 = 14/4 reduces to 7/2

y = mx + b
slope(m) = 7/2
(2,-4)...x = 2 and y = -4
now we sub and find b, the y int
-4 = 7/2(2) + b
-4 = 7 + b
-4 - 7 = b
-11 = b

so ur equation is : y = 7/2x - 11

Equation of line is the equation which tell us about the slope of the line and the intercept of the line at y-axis in the graph. The equation of a line which through the point (2,-4) and (6,10) is,

[tex]y=\dfrac{7}{2} x-11[/tex]

Given-

The points through which the line passes are (2,-4) and (6,10).

What is the equation of line?

Equation of line is the equation which tell us about the slope of the line and the intercept of the line at y-axis in the graph

The equation of a line with a known slope m can also be written as,

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

Here, m is the slope of the line and b is the y intercept on the graph of the line.The formula to find the slope of the line can be given as,

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

[tex]m=\dfrac{10-(-4)}{6-2}[/tex]

[tex]m=\dfrac{14}{4}[/tex]

[tex]m=\dfrac{7}{2}[/tex]

Now the equation of line,

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

[tex][y-(-4)]=\dfrac{7}{2} (x-2)[/tex]

[tex]y+4=\dfrac{7}{2} x-7[/tex]

[tex]y=\dfrac{7}{2} x-7-4[/tex]

[tex]y=\dfrac{7}{2} x-11[/tex]

Hence the equation of a line which through the point (2,-4) and (6,10) is,

[tex]y=\dfrac{7}{2} x-11[/tex]

Learn more about the equation of line here;

https://brainly.com/question/2564656

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