Write the slope intercept form of the equation of the line passing through the points (-2,4) and are perpendicular to the line y=-3x+3.
I just looked back and noticed that drwls had explained to you the relationship between the slopes of perpendicular lines
Isn't the slope of your given line -3 ??
and shouldn't the slope of the new line then be 1/3 ????
let me know what you got.
ok i get it now
i just didn't know what he was saying at first but now I know thanks.
To find the slope intercept form of the equation of a line passing through a given point and perpendicular to another line, we need to follow these steps:
Step 1: Determine the slope of the given line
The given line is y = -3x + 3, which is in the slope-intercept form (y = mx + b), where m is the slope. In this case, the slope is -3.
Step 2: Determine the slope of the line perpendicular to the given line
Since the line we want is perpendicular to the given line, the slope of the perpendicular line will be the negative reciprocal of the given line's slope.
The negative reciprocal of -3 is 1/3.
Step 3: Find the equation of the line using the point-slope form
The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope.
Using the point (-2, 4) and the slope 1/3, we can substitute these values into the point-slope form:
y - 4 = (1/3)(x - (-2))
Simplifying the equation:
y - 4 = (1/3)(x + 2)
Now, let's convert it to the slope-intercept form (y = mx + b):
y - 4 = (1/3)x + 2/3
Adding 4 to both sides:
y = (1/3)x + 14/3
Therefore, the slope-intercept form of the equation of the line passing through the point (-2,4) and perpendicular to the line y = -3x + 3 is y = (1/3)x + 14/3.