Find the equation of the line, in slope-intercept form, that satisfies the given conditions. The graph is perpendicular to the graph of y=3x-1 and passes through the points whose coordinates are (4,-2).
Y=______
slope = -1/3
point-slope form:
y+2 = -1/3 (x-4)
Now rearrange that into slope-intercept form.
To find the equation of a line that is perpendicular to a given line, we need to use the fact that perpendicular lines have slopes that are negative reciprocals of each other.
The given line has a slope of 3. To find the slope of the line perpendicular to it, we take the negative reciprocal of 3, which is -1/3.
Now that we have the slope (-1/3) and a point (4,-2) that the line passes through, we can use the point-slope form of a linear equation. The point-slope form is given by y - y₁ = m(x - x₁), where m is the slope and (x₁,y₁) is a point on the line.
Plugging in the values into the equation, we have y - (-2) = (-1/3)(x - 4).
Simplifying gives y + 2 = (-1/3)(x - 4).
To write the equation in slope-intercept form (y = mx + b), we need to isolate y.
Distributing the -1/3 gives y + 2 = (-1/3)x + 4/3.
Then, subtracting 2 from both sides gives y = (-1/3)x + 4/3 - 6/3.
Simplifying further gives y = (-1/3)x - 2/3.
Thus, the equation of the line, in slope-intercept form, that satisfies the given conditions is y = (-1/3)x - 2/3.