find an equation for the line satisfying the given conditions Y-intercept 8 and perpendicular to 3x-y +11=0
Slope of 3x - y + 11 = 0 is 3
so the slope of your new line is -1/3
can you form the equation of a line with slope -1/3 and y-intercept of 8 ?
What does y = mx + b represent ?
To find an equation for a line that is perpendicular to another line, we need to find the slope of the given line and then apply the relationship that perpendicular lines have slopes that are negative reciprocals of each other.
Let's first rewrite the given line in the slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
To do this, rearrange the equation 3x - y + 11 = 0:
3x - y = -11
-y = -3x - 11
y = 3x + 11
So, the given line has a slope of 3.
Since we want to find a line that is perpendicular to this line, the slope of the new line will be the negative reciprocal of 3, which is -1/3.
Now, we have the slope (-1/3) and the y-intercept (8) for the new line. We can plug these values into the slope-intercept form equation (y = mx + b) to find the equation for the line:
y = (-1/3)x + 8
Thus, the equation for the line satisfying the given conditions (perpendicular to 3x - y + 11 = 0 and y-intercept of 8) is y = (-1/3)x + 8.