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Svetradugi [14.3K]
3 years ago
5

(SHOW WORK) Write the slope-intercept form of the equation:

Mathematics
1 answer:
stiks02 [169]3 years ago
7 0

Answer:

\displaystyle y = -4x - 5

Step-by-step explanation:

We want to find the slope-intercept form of the equation that passes through the point (-2, 3) and is perpendicular to the line:

\displaystyle y = \frac{1}{4} x - 4

Note that this line has a slope of 1/4.

Recall that the slopes of perpendicular lines are negative reciprocals of each other.

Since the slope of our old line is 1/4, the slope of its perpendicular line must be -4.

We are also given that it passes through the point (-2, 3). So, we can consider using point-slope form:

\displaystyle y - y_1 = m(x - x_1)

Let (-2, 3) be (<em>x₁, y₁</em>) and substitute -4 for the slope <em>m</em>. Hence:

\displaystyle y - (3)= -4 (x - (-2))

Convert into slope-intercept form. Simplify:

\displaystyle \begin{aligned} y -3 &= -4 (x + 2) \\ y - 3 &= -4x - 8 \\ y &= -4x -5\end{aligned}

In conclusion, the perpendicular line that passes through the point (-2, 3) is given by:

\displaystyle y = -4x - 5

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