Consider the line y=(7)/(3)x+4. Find the equation of the line that is perpendicular to this line and passes through the point (-7,-5). Find the equation of the line that is parallel to this line and passes through the point (-7,-5).

Question

Consider the line  y=(7)/(3)x+4. Find the equation of the line that is perpendicular to this line and passes through the point  (-7,-5). Find the equation of the line that is parallel to this line and passes through the point  (-7,-5).

Bytelearn · Accepted Answer

Identify slope:  Step 1: Identify the slope of the given line. The equation of the line is y = (7/3)x + 4. This is in the slope-intercept form y = mx + b, where m is the slope. Slope of the given line = 7/3. Find perpendicular slope:  Step 2: Find the slope of the line perpendicular to the given line. The slope of lines that are perpendicular to each other are negative reciprocals. So, the slope of the perpendicular line = -1/(7/3) = -3/7. Use point-slope form:  Step 3: Use the point-slope form to find the equation of the perpendicular line. The point given is (-7, -5). Using the point-slope form y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point, y - (-5) = -3/7(x - (-7)) y + 5 = -3/7(x + 7). Simplify perpendicular equation:  Step 4: Simplify the equation of the perpendicular line. y + 5 = -3/7x - 3 y = -3/7x - 8.

Consider the line $y=\frac{7}{3} x+4$ . $\newline$ Find the equation of the line that is perpendicular to this line and passes through the point $(-7,-5)$ . $\newline$ Find the equation of the line that is parallel to this line and passes through the point $(-7,-5)$ .

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