First the slope. Perpendicular to a slope of -3 means a line slope of 1/3
y= 1/3 x + b.
Now put in the x,y point and solve for b.
write the equation of a line that has a y intercept (0,5) and is perpendicular to the line with equation y=-3x+1
To find the equation of a line that is perpendicular to another line with a given equation, you'll need to follow these steps:
1. Determine the slope of the given line.
In this case, the equation of the given line is y = -3x + 1. The slope of this line is -3.
2. Calculate the perpendicular slope.
The perpendicular slope is the negative reciprocal of the given slope. So, in this case, the perpendicular slope would be 1/3.
3. Use the slope-intercept form of a line (y = mx + b) and substitute the perpendicular slope for the "m" value. Then solve for the y-intercept "b".
The equation becomes:
y = (1/3)x + b
4. Solve for the y-intercept "b" using the given y-intercept point (0,5).
Substitute the x-coordinate (0) and y-coordinate (5) values into the equation and solve for "b".
5 = (1/3)(0) + b
5 = 0 + b
b = 5
5. Substitute the value of "b" back into the equation to get the final equation of the line:
y = (1/3)x + 5
So, the equation of the line that has a y-intercept of (0,5) and is perpendicular to y = -3x + 1 is y = (1/3)x + 5.