write the standard form of the equation of the line through the given point with the given slope. through: (1,2) slope =7

Question

I simply don't get this math, it is too confusing for me

Answer 1

Brenda,

It's really not that bad. Let me walk you through the essentials. First, take some graph paper, draw x and y axes, and graph the point (1,2) [I assume you know how to do that?]. Now if there is a line with slope 7 that passes through that point, that means that every time you move one unit in the x direction along that line, your y value changes by 7 units from what it was. (that's what slope is defined as!) So, start at the point (1,2). Your x value here is 1. If you move on the sloped line back to x=0, that's a change of -1 unit (change is always {final-initial}, so it will be negative in this case). Since the slope of the line tells you that your y value needs to change by 7 times as much, it must have changed by -1*7=-7 units. So if you started at y=2, you are now at y=2-7=-5 location. So you are on the plane at the point (0,-5). Graph this point also. Draw a line between your two graphed points: that's your line. The standard form for a line is an equation of the form of y=mx + b, where m = the slope (you already know this is 7), and b = the y-intercept of the line == the y-value of the place where the line crosses the y-axis. But you just graphed this as -5; so your total equation ends up as:

 

y = 7x +(-5) or y = 7x - 5

 

Note that "x" in the above equation stands for the variable x, not for the multiplication symbol! In both math and science, letters are sometimes used in multiple ways; so if you have an equation with both the variable "x" and a multiplication symbol, it might be wise to get into the habit of using the centered dot (like a decimal point, but centered midway up the letter height) for the multiplication sign, instead of an "x". That reduces the potential for confusion.

 

Answer 2

Hello, Brenda from California

 

Great weather.. I love California..

 

Well, you can do this problem a couple different ways, but let us use the POINT-SLOPE FORM.  You might recall that the formula is y-y1=m(x-x1), where m= the slope and (x1,y1) is the point that the line passes through. Note the other y and the other x do not have a value.  They are part of the formula.  Ok, substituting into the equation.

 

y-y1=m(x-x1)

y-(2)=7[x-(1)]                       Using the distributive property.

y-2  = 7x-7                       Adding 2 to both sides

  +2        +2

      y= 7x -5                    Subtract 7x from both sides

    -7x  -7x

-7x+y =-5.                      Multiplying by -1 both sides

 7x-y  =5.                       This is the STANDARD FORM: AX+BY=C

 

I hope this helps out a little and don't forget to rate my answer.

 

D. Y. T.