Find an equation of the line that passes through the given points.
Finding the equation of a line
The equation of a line is given by the formula y= mx+b.
This is known as the slope-intercept form of a linear equation. It is called a linear equation because when you graph this equation all of the points make a straight line.
In this equation m = slope. The slope = rise over run or "change in y over change in x.
To find the slope you would use the formula m=y2-y1/x2-x1
We will label our points: X1=-13, X2=20, Y1= 13, Y2=-53
We will insert the points into our formula , m= (-53)- 13/20-(-13) = -66/33=
Therefore our slope is m= -2
Next we need to find b which is the y-intercept. This is the value of y when x = 0
To find the y intercept, we can use 2 methods:
• Method 1:
Since we know the points and the slope, we can plug one pair of them (it doesn't matter which pair) into our equation y-mx +b, We will use the points (-13,13)
13 =-2(-13) +b)
We will subtract 26 both sides to isolate b.
-13 =b (Therefore b or the "y-intercept=-13)
• Method 2
Since we know the points and the slope, we can use the point-slope formula to find the y -intercept.
The point-slope formula is y-y1= m(x-x1) We will use the points (13,-13, the points we have identified as (x1,y1), Again we could have used either pair.
Y-13= -2(x-(-13) )
We will add 13 to both sides to isolate Y
Y= -2x-13 (Therefore b or the "y-intercept=-13)
Therefore the equation of the line is: Y= -2X-13
To verify our solution we will substitute both set of points into the equation.
• 13 = -2(-13)-13
• 13= 26-13
- -53 = -2(20)-13
- -53 = -40 - 13
- -53= -53
We have verified our equation of the line, y= -2x-13
M (Slope) = -2
B (Y-Intercept) = -13
The equation of a line is given by y=mx+b where m is the slope and b is the y-intercept.
First, to solve for the slope, use "rise over run," or "y over x:" m=(y2-y1)/(x2-x1) where (-13, 13) is the first point and (20, -53) is the second point. Thus, after substituting the values into the equation, you would have m=(-53-13)/[20-(-13)].
Next, to solve for the y-intercept, insert the value found for m into y=mx+b. Then, substitute the x and y values of just one of the given points into the same equation. For example, -53=m(20)+b or 13=m(-13)+b are both viable options. After solving for b, you can then substitute that value into y=mx+b.
To check your answer, plug one of the given points back into y=mx+b. Both sides of the equal sign should be equal.
We are looking to fill in the basic equation of a line: y=mx+b
m=slope and b=y-intercept
First, we will find the slope by using the equation: (y2-y1)/(x2-x1)
In this case y2=-53 y1=13 x2=20 x1=-13
Fill in those points into the slope equation. (-53-13)/(20-(-13)) = -66/33 = -2
Now, we will plug in one of the points listed above either (-13, 13) or (20, -53) and plug it into the equation: y=-2x+b
Finally, the equation for the line that passes through the given points (-13, 13) and (20, -53) is: