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What is the equation in slope-intercept form of the line that passes through the points (−26, −11) and (39, 34)?
A) y = − 9 13 x + 7
B) y = − 9 13 x − 7
C) y = 9 13 x + 7
D) y = 9 13 x − 7

Sagot :

Lanuel

The equation in slope-intercept form of the line passing through the given points is: C. [tex]y = \frac{9}{13}x + 7[/tex]

Given the following points:

  • Points on the x-axis = (-26, 39)
  • Points on the y-axis = (-11, 34)

To find the equation in slope-intercept form of the line passing through the given points:

Mathematically, the equation of slope is calculated by using this:

[tex]Slope. \;m = \frac{Change \; in \; y \;axis}{Change \; in \; x \;axis} \\\\Slope. \;m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Substituting the given points, we have:

[tex]Slope. \;m = \frac{34 - [-11]}{39 - (-26)}\\\\Slope. \;m = \frac{34\; + \;11}{39 \;+ \; 26}\\\\Slope. \;m = \frac{45}{65}\\\\Slope. \;m = \frac{9}{13}[/tex]

The standard form of an equation of line is given by the formula;

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

Where:

  • x and y are the points.
  • m is the slope.
  • b is the intercept.

We would find the intercept:

[tex]-11 = \frac{9}{13}(-26) + b\\\\ -11 = -18 + b\\\\b = -11 + 18[/tex]

Intercept, b = 7

The equation in slope-intercept form of the line is:

[tex]y = \frac{9}{13}x + 7[/tex]

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