Respuesta :

texaschic101
2x - 3y = 6
-3y = -2x + 6
y = 2/3x - 2....the slope here is 2/3. A parallel line will have the same slope

y = mx + b
slope(m) = 2/3
(9,-3)...x = 9 and y = -3
now we sub and find b, the y int
-3 = 2/3(9) + b
-3 = 6 + b
-3 - 6 = b
-9 = b

so ur parallel equation is : y = 2/3x - 9 <== or 2x -3y = 27
akposevictor

The equation of the line, in slope-intercept form, that is parallel to 2x - 3y = 6 and passes through (9, -3) is: [tex]\mathbf{y = \frac{2}{3}x - 9}[/tex]

Given:

Points the line passes through, (9, -3)

The equation of the line it is parallel to: 2x - 3y = 6

Note:

  • Parallel lines have the same slope value
  • Equation of a line in slope-intercept form is: y = mx + b. (m is slope; b is y-intercept)
  • Point-slope form is; y - b = m(x - a)

First, rewrite 2x - 3y = 6 in slope-intercept form to determine its slope.

[tex]2x - 3y = 6\\\\-3y = -2x + 6\\\\y = \frac{2}{3}x - 2[/tex]

  • The slope of 2x - 3y = 6 is therefore 2/3.

Thus, the slope of the line that passes through (9, -3) is also 2/3.

Write the equation of the line in point-slope form:

Substitute m = 2/3, and (a, b) = (9, -3) into y - b = m(x - a)

  • Thus:

[tex]y - (-3) = \frac{2}{3}(x - 9)\\\\y + 3 = \frac{2}{3}(x - 9)[/tex]

  • Rewrite in slope-intercept form

[tex]y + 3 = \frac{2}{3}(x - 9)\\\\y + 3 = \frac{2}{3}x -\frac{2}{3}(9)\\\\y + 3 = \frac{2}{3}x - 6\\\\y = \frac{2}{3}x - 6 - 3\\\\\mathbf{y = \frac{2}{3}x - 9}[/tex]

Therefore, the equation of the line, in slope-intercept form, that is parallel to 2x - 3y = 6 and passes through (9, -3) is: [tex]\mathbf{y = \frac{2}{3}x - 9}[/tex]

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