Question

Write the slope-intercept form of the equation that passes through the point (-1, 2) and is perpendicular to the line y = 3/2x + 6

Answer 1

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Answer:  $\textsf{y = -2/3x + 4/3}$

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Given:  $\textsf{Passes through (-1, 2) and perpendicular to y = 3/2x + 6}$

Find:  $\textsf{The equation in slope-intercept form}$

Solution: We need to figure out the equation in slope-intercept form and the first step is to understand the slope.  We know that it is going to be perpendicular to 3/2 and in order to find the perpendicular slope we must first negate it.  We would then take the reciprocal of that number and in this case the slope would be -2/3.  After that we just plug into the point-slope formula, simplify, distribute, and solve for y.

Plug in the values

• $\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}$

• $\textsf{y - 2 = -2/3(x - (-1))}$

Simplify and distribute

• $\textsf{y - 2 = -2/3(x + 1)}$

• $\textsf{y - 2 = (-2/3 * x) + (-2/3 * 1)}$

• $\textsf{y - 2 = -2/3x - 2/3}$

Add 2 to both sides

• $\textsf{y - 2 + 2 = -2/3x - 2/3 + 2}$

• $\textsf{y = -2/3x - 2/3 + 2}$

• $\textsf{y = -2/3x + 4/3}$

Therefore, after completing the steps we were able to determine that the equation the best fits the description that was provided is y = -2/3x + 4/3.