I need to know what the equation of a line that is perpendicular to y= -3x+4 and has (0,2)?

Answer 1

The first line has a slope of -3 (by inspection and knowing the slope-intercept form).

A perpendicular line will have a slope equal to the *negative reciprocal*. The negative reciprocal of -3 is 1/3.

Now the problem reduces to "give the equation of a line with slope 1/3 through point (0,2)".

Use the point slope form of a line:
y - y1 = m(x - x1)

m = 1/3
x1 = 0
y1 = 2

Therefore:
y - 2 = (1/3)(x - 0)
y - 2 = (1/3)x

Solving in terms of y:
y = (1/3)x + 2

Answer 2

y = x/3 + 2

Answer 3

to find a line that is perpendicular to another line, you take the negative reciprocal of the slope of the first line. so in your first line, the slope is -3/1, and the the negative reciprocal is 1/3. then you need to find the y-interecept. that means the y-value when x= 0, which is given in the coordinate point in the problem. you know that there is only one y-int in a linear graph. therefore you jsut plug this into the point slope formula. a=mx+b, where m is the slope and b is the y-int. the equation is y=1/3(x)+2