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:
To write the equation of the line that passes through (-1, 2), we need to find the slope value.
[tex]\frac{2y}{2} = \frac{2x}{2} - \frac{1}{2} \\\\y = x - \frac{1}{2}[/tex]
[tex]y - 2= -1(x - (-1))\\\\y - 2 = -1(x + 1)[/tex]
[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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