find the line that is perpendicular to the line y=1/3x+4 and contains the point (-9,0)
By this time, you ought to have some idea of how to solve these line problems. Whatcha got?
To find a line that is perpendicular to a given line, we need to determine the slope of the given line first. The given line is y = 1/3x + 4, which is in slope-intercept form (y = mx + b) where m is the slope.
In this case, the slope of the given line is 1/3.
To find a line perpendicular to this, we need to find the negative reciprocal of the slope. The negative reciprocal of 1/3 is -3/1 or -3.
Now we have the slope (-3) and a point (-9, 0). We can use the point-slope form of a line (y - y₁ = m(x - x₁)) to find the equation of the line.
Substituting the values, we get:
y - 0 = -3(x - (-9))
Simplifying, we have:
y = -3(x + 9)
So, the line that is perpendicular to y = 1/3x + 4 and contains the point (-9, 0) is y = -3(x + 9).