What is the equation of a line that is perpendicular to the line that goes through the points (0, -3) and (-3, 12)?
Can you please give me the steps to solve this. I got m which is -5, but I don't know what to do next.
well, your original line through the points has
m = 15/-3 = -5 as you said
so the perpendicular line has slope
m' = -1/m = -1/-5 = +0.2
It could hit the original line anywhere so we can not find b without a point on the new line.
so
y = 0.2 x + b
is the best we can do.
Is there a part B where you put that through a point?
There were four answers
A: y = 15x + 2
B:y = (-1/15x) - 8
C: y = -9x - 7
D: y = (1/5x) - 3
The answer would be D then, but I still don't understand. Is the perpendicular line's slope always the reciprocal of the original slope?
To find the equation of a line that is perpendicular to another line, you need to consider the slope of the original line.
First, determine the slope of the line passing through the points (0, -3) and (-3, 12). The slope (m) can be calculated using the formula:
m = (y2 - y1)/(x2 - x1)
Let's substitute the coordinates into the formula:
m = (12 - (-3))/(-3 - 0)
m = 15/(-3)
m = -5
Good job! You correctly calculated the slope of the line passing through the given points as -5.
Next, remember that for two lines to be perpendicular, their slopes should be negative reciprocals of each other. In other words, if the slope of the original line is m, then the slope of the perpendicular line is -1/m (or 1/m if we want the negative reciprocal).
Since the slope of the original line is -5, the slope of the line perpendicular to it would be -1/(-5) = 1/5.
Finally, we can use the point-slope form of a linear equation to find the equation of the perpendicular line. The point-slope form is:
y - y1 = m(x - x1)
We can choose any point on the line, such as (0, -3), and substitute the slope m = 1/5. Applying the point-slope form, we have:
y - (-3) = (1/5)(x - 0)
y + 3 = (1/5)x
Now, we can rearrange the equation to the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept:
y = (1/5)x - 3
So, the equation of the line perpendicular to the line passing through (0, -3) and (-3, 12) is y = (1/5)x - 3.