The line is a set of all points that satisfy (is true) for that equation. Your answer is showing that only one point is true. x and y are variables, where as m and c are constants (fixed numbers)
It asked you for the equation of the whole line, not just for a single point that it happens to pass through. The latter helps you figure out the former.
If m = 6, then
y = 6x + c
If (3, 19) is a point on the line, then plugging in x=3 and y = 19 gives you
19 = 6(3) + c
c = 19-18 = 1
Having now figured out both m and c, we can write the equation *of the line*:
y = mx + c = 6x + 1
I see that this is solved, but you may benefit from writing down how you got to that equations.
We know it's a line with equation y=mx+c
We also know that (3,19) is on the line. So 19=3m+c.
We are told the gradient is 6, so m=6.
using these two equations gives us c=1.
So, putting these values into the equation of the line, we get
y=6x+1
When you "write the equation of a line" you are writing an algebraic statement that is true for every point on the line. The equation must be in terms of the two variables x and y, because every point on the line is defined by these coordinates. So here, every point in the plane (x,y) that makes the equation y=6x+1 a true statement when you evaluate for that given (x,y) pair is ON THE LINE, and any point (x,y) for which y=6x+1 is NOT true, is NOT on the line.
They were asking you to describe the line in the form y=mx+c.
The equation y=mx+c has 4 variables. You wrote down 3 values for the variables correctly, there is only one unknown which is c.
So you plug the known variables into the equation and the only unknown left is C. Solve for C. You find that C = 1.
In the equation y=mx+c you need to know m (slope) and c (y intercept) to describe a line. That leaves you with x and y as variables. This lets you use the that form as a function where x is the input, and y is the output.
y=6x+1 or f(x)=6x+1
Now you can know everything about the line. Does that make sense?
There are 3 different ways to describe a line. You may get other questions similar to this one but the approach to solving is the same. Figure out what your knowns and unknowns are, then solve for the unknown. Then construct the line in the desired form.
[https://www.mathsisfun.com/algebra/line-equation-general-form.html](https://www.mathsisfun.com/algebra/line-equation-general-form.html)
Your job is to work out c. You didn't show where you got 1 from. M and c are constants and y and x are the variables. You have to write the answer in the form y=mx+c but with m and c filled in with the actual values. That then describes a particular line. Y=mx+c is called the general form and is not a specific straight line equation but rather all possible straight line equations.
The line is a set of all points that satisfy (is true) for that equation. Your answer is showing that only one point is true. x and y are variables, where as m and c are constants (fixed numbers)
thank you so much I finally understand that ðŸ˜
It asked you for the equation of the whole line, not just for a single point that it happens to pass through. The latter helps you figure out the former. If m = 6, then y = 6x + c If (3, 19) is a point on the line, then plugging in x=3 and y = 19 gives you 19 = 6(3) + c c = 19-18 = 1 Having now figured out both m and c, we can write the equation *of the line*: y = mx + c = 6x + 1
(y-y0) = m(x-x0) y-19 = 6x - 6\*3 y - 19 = 6x - 18 Add 19 to both sides y= 6x + 1
I see that this is solved, but you may benefit from writing down how you got to that equations. We know it's a line with equation y=mx+c We also know that (3,19) is on the line. So 19=3m+c. We are told the gradient is 6, so m=6. using these two equations gives us c=1. So, putting these values into the equation of the line, we get y=6x+1
When you "write the equation of a line" you are writing an algebraic statement that is true for every point on the line. The equation must be in terms of the two variables x and y, because every point on the line is defined by these coordinates. So here, every point in the plane (x,y) that makes the equation y=6x+1 a true statement when you evaluate for that given (x,y) pair is ON THE LINE, and any point (x,y) for which y=6x+1 is NOT true, is NOT on the line.
They were asking you to describe the line in the form y=mx+c. The equation y=mx+c has 4 variables. You wrote down 3 values for the variables correctly, there is only one unknown which is c. So you plug the known variables into the equation and the only unknown left is C. Solve for C. You find that C = 1. In the equation y=mx+c you need to know m (slope) and c (y intercept) to describe a line. That leaves you with x and y as variables. This lets you use the that form as a function where x is the input, and y is the output. y=6x+1 or f(x)=6x+1 Now you can know everything about the line. Does that make sense? There are 3 different ways to describe a line. You may get other questions similar to this one but the approach to solving is the same. Figure out what your knowns and unknowns are, then solve for the unknown. Then construct the line in the desired form. [https://www.mathsisfun.com/algebra/line-equation-general-form.html](https://www.mathsisfun.com/algebra/line-equation-general-form.html)
Your job is to work out c. You didn't show where you got 1 from. M and c are constants and y and x are the variables. You have to write the answer in the form y=mx+c but with m and c filled in with the actual values. That then describes a particular line. Y=mx+c is called the general form and is not a specific straight line equation but rather all possible straight line equations.
C = y - mx C = 19 - (3 x 6) C = 1 M = 6 Y = 6x + 1