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find the slope intercept form of the line satisfying the following conditions. x- intercept 2 and y intercept 1/3

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3 Answers

The slope-intercept form is a way of describing a line that is designed to make two pieces of information immediately available: the slope (m), and the y-intercept (b). You will need these to pieces of information to put the line in slope-intercept form: y=mx + b

The y-intercept (b) is already given to you: 1/3.

The only remaining task is to find the slope (m). The slope of any line can be found just by using two points on that line, using the formula (y2-y1)/(x2-x1). The two points we are given are the x-intercept, (2,0), and the y-intercept, (0, 1/3). Plugging this into the slope formula, we get (1/3 - 0)/(0 - 2), which is equal to (1/3)/(-2), which in turn equals -1/6.

Now we just plug our slope (m) and y-intercept (b) into the slope-intercept form (y=mx+b). From this, we get y = (-1/6) x + 1/3.

The information you are given tells you the coordinates of two points on the line. An x-intercept of 2 means that the line crosses the x-axis at the point (2, 0). The y-intercept is the point (0, 1/3).

Use the slope formula m = (y2 - y1)/(x2 - x1). You have to decide which point is point 1 and which is point 2. It will work whichever you choose as long as you substitute into the formula correctly.

I choose (2, 0) to be point 1 and (0, 1/3) to be point 2. x1=2, y1= 0, x2=0, y2=1/3.

Substitute into the formula and m= (1/3 - 0)/(0 - 2), so m = (1/3) / -2,  m = -1/6

The equation of the line is in the form y = mx + b, where m is the slope and b is the y-intercept.

We just found m = -1/6 and we were given b = 1/3 so put these into the correct place in the equation and we get y = (-1/6)x + (1/3) as the equation of the line.

Coordinates of x-intercept are (x, 0) 
Coordinates of y-intercept are (0, y)
Slope-intercept form of the linear equation is
y = mx + b ("m" is slope of the line, "b" is y-intercept)
~~~~~~~~~~
Given: (2, 0) and  1/3  as y-intercept.
Let's find slope of the line
0 = m • 2 + 1/3
            1
m = – ——
            6

y = – (1/6) x + 1/3