Respuesta :

texaschic101
(3,2),(-9,6)
slope = (6 - 2) / (-9 - 3) = -4/12 = -1/3

y = mx + b
slope(m) = -1/3
use either of ur points...(3,2)....x = 3 and y = 2
now we sub into the formula and find b, the y int
2 = -1/3(3) + b
2 = -1 + b
2 + 1 = b
3 = b
so ur equation is : y = -1/3x + 3 <==
akposevictor

The equation in slope-intercept form that represents the line is: [tex]y = -\frac{1}{3}x + 3[/tex]

Given:

[tex](3, 2)\\(9, 6)[/tex]

  • The slope-intercept equation of a line that passes some set of points is given as:

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

[tex]where,\\\\slope = m\\\\y-intercept = b\\[/tex]

  • We need to find the values of b and m.

  • Find slope (m):

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

Let,

[tex](3, 2) = (x_1, y_1)\\(-9, 6) = (x_2, y_2)[/tex]

Plug in the values

[tex]m = \frac{6 - 2}{-9-3} = \frac{4}{-12} \\\\m = -\frac{1}{3}[/tex]

  • Find the value of b.

Substitute m = -1/3 and (x, y) = (3, 2) into [tex]y = mx + b[/tex]

Thus:

[tex]2 = -\frac{1}{3} (3) + b\\\\2= -1 + b\\\\2 + 1 = b\\\\3 = b\\\\b = 3[/tex]

Write the equation by substituting m = -1/3 and b = 3 into [tex]y = mx + b[/tex]

[tex]y = -\frac{1}{3}x + 3[/tex]

The equation that represents the line is therefore [tex]y = -\frac{1}{3}x + 3[/tex]

Learn more here:

https://brainly.com/question/16732089

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