find the equation of this straight line, m=3, passing through (1,4)
find the equation of straight lines
Recall the slope=intercept form of a linear equation: y = mx + b , where m is the slope of the line and b is the y-intercept (point at which line crosses y-axis: (0, b) )
Given: slope = m = 3
(x, y) = (1, 4) ==> x = 1 , y = 4
y = mx + b
4 = 3(1) + b
4 = 3 + b
4 - 3 = 3 - 3 + b
1 = b
Therefore, given that the slope= m= 3 and the y-intercept= b= 1, the equation of the line is as follows:
y = 3x + 1
To solve this linear equation, we want to state it in the slope-intercept form which is y=mx+b
m= slope, b=y intercept
Since we already know the slope and we have a pair of coordinates, you can utilize the point-slope form of the equation to solve it.
The point slope form is: y-y1= m(x-x1) m=3, (x1=1, y1=4)
Therfore Y-4= 3(x-3)
Use the distributive property to simplify the right side,
Add 4 to both sides to isolate y
The final result is Y= 3X+1. (This is the equation in slope intercept form.)
We know that the equation should be written in the form y=mx + b, where m is the slope and b is the y intercept. Start by graphing the x and y axis, as well as the point (1.4). Since m is 3. we know that that is the slope, and that it is positive. Three is the value of the rise/run. Since our rise/run must be positive we can use that information to graph a few more points: go up 3 and to the right 1, (both positive values) OR go down 3 and to the LEFT one (both negative values). We get the "B" value where x =0: i.e., where our line crosses the y axis, which it does at (0,1) Since the "y" in this ordered pair is equal to one, we now have our equation: y=3x + 1.
Start with the equation (y-4)= 3(x-1). Use the distributive property to multiply the 3 by (x-1), yielding this: (y-4)=3x-3. Then get y by itself by adding 4 to both sides, getting this: y=3x+1. There you have the equation in slope intercept form. If your teacher wants it in standard form (Ax +By=C), then just work from there, by subtracting the 3x from both sides, yielding -3x+y=1. Hope this helps.