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Find the equation of the line that passes through (-1,2) and is perpendicular to 2 y = 2 x − 1 . Leave your answer in the form y = m x + c

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akposevictor

The equation in slope-intercept form of the line that passes through the point (-1, 2) and is perpendicular to the line equation, [tex]2 y = 2 x - 1[/tex] is: [tex]y = -x + 1[/tex]

Recall:

Equation of a line in slope-intercept form is: [tex]y = mx + c[/tex], where, slope = m, and y-intercept = c.

Point-slope form is: [tex]y - b = m(x - a)[/tex]

The slope value of a line will be the negative reciprocal of the slope of the line it is perpendicular to. i.e. if the slope of a line is a, the slope of the line that it is perpendicular to will be -a.

Given:

  • The line passes through point (-1, 2)

  • Equation of line it is perpendicular to is: [tex]2 y = 2 x - 1[/tex]

To write the equation of the line that passes through (-1, 2), we need to find the slope value.

  • First, rewrite  [tex]2 y = 2 x - 1[/tex] and find its slope.

[tex]\frac{2y}{2} = \frac{2x}{2} - \frac{1}{2} \\\\y = x - \frac{1}{2}[/tex]

  • The slope (m) of [tex]2 y = 2 x - 1[/tex] is therefore 1.

  • Thus, the slope (m) of the line that passes through (-1, 2) will be the negative reciprocal of 1 = -1.

  • Write the equation of the line by substituting (a, b) = (-1, 2) and m = -1 into  [tex]y - b = m(x - a)[/tex]:

  • Thus:

[tex]y - 2= -1(x - (-1))\\\\y - 2 = -1(x + 1)[/tex]

  • Rewrite this in the form of [tex]y = m x + c[/tex]

  • Thus:

[tex]y - 2 = -x - 1\\\\y = -x - 1 + 2\\\\y = -x + 1[/tex]

Therefore, the equation in slope-intercept form of the line that passes through the point (-1, 2) and is perpendicular to the line equation, [tex]2 y = 2 x - 1[/tex] is [tex]y = -x + 1[/tex]

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