Respuesta :

texaschic101
slope formula : (y2 - y1) / (x2 - x1)
(2,-2)....x1 = 2 and y1 = -2
(4,1)...x2 = 4 and y2 = 1
now we sub into the slope formula and solve for the slope
slope = (1 - (-2) / (4 - 2) = (1 + 2) / 2 = 3/2

now we use y = mx + b
slope(m) = 3/2
use either of ur points....(4,1)...x = 4 and y = 1
now sub into y = mx + b formula and find b, the y int
1 = 3/2(4) + b
1 = 6 + b
1 - 6 = b
-5 = b

so ur equation is : y = 3/2x - 5 <==

akposevictor

The equation, in slope-intercept form, of the line that passes through points (2,-2) and (4,1), is: y = 3/2x - 5.

Recall:

  • Equation of a line in slope-intercept form is: y = mx + b, where, slope = m, and b = y-intercept
  • Equation of a line in point-slope form is: y - b = m(x - a), where, m = slope and (a, b) = a point.
  • Slope (m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Given:

(2,-2) and (4,1)

  • Find the slope:

[tex]Slope (m) = \frac{1 - (-2)}{4 - 2} = \frac{3}{2} \\\\\mathbf{Slope(m) = 3/2}[/tex]

  • Write the equation in point-slope form by substituting m = 3/2 and (a, b) = 4, 1) into y - b = m(x - a)

y - 1 = 3/2(x - 4)

  • Rewrite in slope-intercept form

y - 1 = 3/2(x) - 3/2(4)

y - 1 = 3/2x - 6

y = 3/2x - 6 + 1

y = 3/2x - 5

Therefore, the equation, in slope-intercept form, of the line that passes through points (2,-2) and (4,1), is: y = 3/2x - 5.

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