How can you figure out the linear equation when only given 1 point and the slope, for example (1,3), m=4?

Please be detailed. I am not looking for answers to my homework but an understanding!





Shawn C.





dell_email Yahoo IDHow can you figure out the linear equation when only given 1 point and the slope, for example (1,3), m=4?
A straight line (linear equation) requires either...


a) two points (and then join them up), or


b) one point and an indication of the direction (which is the gradient).





The equation of a line is y = mx + b where,


y is the y-coordinate


x is the x-coordinate


m is the gradient


b is the y-intercept location





Your question gives 3 out of 4 of these values.


The point (1,3) has the values x = 1, y = 3


The gradient has the value m = 4


By substitution then,


y = mx + b


3 = 4 x 1 + b


3 = 4 + b


-1 = b


Therefore, the equation of the line is


y = 4x - 1





Another example, find the linear equation given the point (4, 3) and gradient (m) = -1


y = mx + b


x = 4, y = 3, m = -1, find b


3 = -1 x 4 + b


3 = -4 + b


7 = b


Therefore, the equation is


y = -1x + 7, or


y = -x + 7





If you are given two points, say (2, 5) and (3, 4), you could perform the following:


a) find the gradient (m = (y2 - y1) / (x2 - x1)) then use 1 point to find the y-intercept (b)


b) use the point-gradient formula: y - y1 = m(x - x1)





Trust this helps.How can you figure out the linear equation when only given 1 point and the slope, for example (1,3), m=4?
y-y1=m(x-x1) is point-slope form. To get it into the form you probably want:


y=mx-m(x1)+y1


y=4x-4*1+3


y=4x-1
Let (x1, y1) = (1, 3) be the point on the line and the slope is m = 4.


The, the equation of the line given one point and the slope is given by: y - y1 = m(x - x1)


=%26gt; y - 3 = 4(x - 1)


=%26gt; y - 3 = 4x - 4


=%26gt; y - 3 + 3 = 4x - 4 + 3


=%26gt; y = 4x - 1


=%26gt; 4x - y - 1 = 0 is the required line
Use the point-slope formula.





y-y1=m(x-x1) where m=slope, and x1 and y1 are the given point.





y-3=4(x-1)


y=4x-4+3


y=4x-1