Math- Algebra 1

Question

Write the equation of the line perpendicular to the graph of the given equation and passes through the given point.

Perpendicular to y = 1/3x + 2 and passes through (2,-1)

Answer 1

y=(1/3)x + 2 has slope =1/3. The slope is the coefficient of the x term when the linear equation is solved for y

a perpendicular line has a negative inverse slope = -3. Just take 1/3, flip it upside down and change its sign

y=-3x + b is the perpendicular line's equation. to find b, plug in the point (2,-1)

-1 =-3(2)+b

b =-1+6 = 5

y=-3x +5 is the perpendicular line through (2,-1)

Answer 2

Remember that in the equation y = mx + b, m represents the slope of the line and b represents the y-intercept of the line.

To find the equation of line that is perpendicular to a given line, the first step is to identify the slope of your given line. The given line is y = 1/3x + 2. The slope of the line is the coefficient of x (the number in front of x), so the slope of the given line is 1/3.

(The y-intercept of the given line won't matter when figuring out the rest of the question.)

The slopes of perpendicular lines are NEGATIVE RECIPROCALS of each other. That means that the slope of the line that is perpendicular to our given line is -3, so we can substitute that into the slope-intercept form directly, and now we have y = -3x + b.

The line is supposed to pass through (2, -1), so we will substitute this coordinate in the (x, y) of the equation:

-1 = -3(2) + b

-1 = -6 + b

5 = b

So the equation of the PERPENDICULAR line is y = -3x + 5