Question

the equation of the line that is perpendicular to the line with equation y=-2x-1 and passes through the point (1, -2) is?

Answer 1

Answer:

$y=\frac{1}{2} x-\frac{5}{2}$

Step-by-step explanation:

Hi there!

Note that:

• Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
• Perpendicular lines always have slopes that are negative reciprocals of each other (ex. 3 and -1/3, 5/6 and -6/5, etc.)

1) Determine the slope (m)

When we look at the given line, $y=-2x-1$, we can identify that -2 is in the place of m, the slope of the line. Because perpendicular lines are negative reciprocals of each other, we know that a line perpendicular to this would have a slope of $\frac{1}{2}$. Plug this into $y=mx+b$:

$y=\frac{1}{2} x+b$

2) Determine the y-intercept (b)

$y=\frac{1}{2} x+b$

Plug in the given point (1,-2)

$-2=\frac{1}{2}(1)+b\\-2=\frac{1}{2}+b$

Subtract 1/2 from both sides

$-2-\frac{1}{2}=\frac{1}{2}+b-\frac{1}{2}\\-\frac{5}{2} = b$

Therefore, the y-intercept of the line is $-\frac{5}{2}$. Plug this back into $y=\frac{1}{2} x+b$

$y=\frac{1}{2} x-\frac{5}{2}$

I hope this helps!