Give the equation of the line that is perpendicular to the line y= -3x + 7 and passes through point (0, -6)
please help
your new line must have a slope of 1/3
so your new equation is
y = (1/3)x + b
sub in the given point to find b
I still don't understand this?
Have you not learned that the slopes of perpendicular lines are opposite reciprocals ??
So if one slope is -3 , the other is +1/3
How would I get B?
Plug the co-ordinates that you were given into the equation, and then you will only have 1 variable to solve for, which is b.
To find the equation of the line that is perpendicular to the line y = -3x + 7 and passes through the point (0, -6), you need to follow these steps:
Step 1: Determine the slope of the given line
In the equation y = -3x + 7, you can see that the coefficient of x is -3. This represents the slope of the line. The slope-intercept form of a line is y = mx + b, where m is the slope. So, the slope of the given line is -3.
Step 2: Find the perpendicular slope
Since you are looking for a line perpendicular to the given line, you need to find the negative reciprocal of the original slope. To do this, simply flip the fraction and change its sign. In this case, the slope of the new line will be 1/3.
Step 3: Substitute the values in the point-slope form
The point-slope form of a line is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Here, the point given is (0, -6), and the slope is 1/3. Substituting these values, we get:
y - (-6) = (1/3)(x - 0)
Step 4: Simplify the equation
Simplifying the equation gives:
y + 6 = (1/3)x
Step 5: Convert to slope-intercept form
To convert the equation to slope-intercept form (y = mx + b), isolate y by subtracting 6 from both sides:
y = (1/3)x - 6
So, the equation of the line perpendicular to y = -3x + 7 and passing through (0, -6) is y = (1/3)x - 6.