A line passes through the point (0, 2) and has a slope of -1/2. What is the equation of the line?

Question

A line passes through the point (0, 2) and has a slope of -1/2. What is the equation of the line?

Answer 1

Typically you want to translate an equation into the "slope intercept" form y=mx+b, where y is your equation, also known as f(x), m is your slope (in this case -1/2) and b is your y-intercept (the y-value when x=0, given here by the point (0,2)). So all you have to do is write y=-1/2x+2 to find the equation of the line. 

Answer 2

There are several forms for the equation of a line: the two most common are point-slope and slope-intercept.

Point-slope form uses a point and the slope to get the equation.

The equation for the line is y-y₀=m(x-x₀). The slope of the line is m, and a point on the line is (x₀,y₀).

Slope-intercept form uses the slope and the y-intercept to get the equation.

The equation for the line is y=mx+b. The slope of the of the line is m, and the y-intercept is b. (The y-intercept is the point where the line crosses the y-axis.)

 

In the case of this problem, we have a point and a slope, so we want to use the point slope form.

We can simply plug in the numbers to get y - 2 = -1/2(x - 0). This simplifies to y - 2 = -1/2 x, which is the equation of the line. 

Typically, however, people want the equation in slope-intercept form. This means that we need to solve for y, meaning we need to rewrite the equation so that it looks like y=something. In our case, if we add 2 to both sides of the equation, we are left with y = -1/2 x + 2, which is the slope intercept form of the equation for the line.

Answer 3

hint: the y.intercept is 2; the slope is given.  You can answer it easily in the slope-intercept form or the point - slope form.

 

But just for fun, let's track down the x intercept.  Then you might want to write the equation in Standard Form.

 

The slope is rise/run = -1/2, so as the line moves to the right 2 units, it moves down 1 unit.

 

Starting from (0,2) and moving to the right 2 units, the line goes down 1 unit to the point (2,1).

Again moving on by going 2 units right and down one unit, the line intersects the x.axis at (4,0).

 

For standard form, Ax + By = C,

 

find C:  C = the x.intercept times the y.intercept

 

So we have Ax + By = 8

 

When y = 0, at the x intercept, x = 4, and A would have to be 2 so that A(4) + B(0) = 8.

When x = 0, at the y intercept, y = 2, and B would have to be 4 so that A(0) + B(2) = 8.

 

So A = 2 and B = 4 for your standard form.