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changchengliang eNotes educator| Certified Educator
Observing the equation, y=5x-6, It is a linear equation of the form y=mx+c, Where m is the gradient (5 in this case) And c is the y-intercept (-6 in this case) The solution to the graph (ie when y=0) is when x=6/5 (obtained by letting y=0 and making x the subject)
giorgiana1976 | Student

The given expression of the function f(x) = y=mx+n represents a linear function, so it's graph is a straight line.

In order to build the graph, you have to plug in values for x, and find the values for y.

For drawing the the graph, it's necessary to get two points. That means having 4 coordinates. You know that a point is defined by its coordinate (x,y).


We'll put x = 0.

y = 5*0 -6

y = -6

The point has the following coordinates: (0,-6)

We'll put x = -1

y = 5*(-1) -6=-5-6=-11

The point has the following coordinates: (-1,-11)

Now, in order to draw the graph, we'll draw x,y rectangular system of axis. 0x is perpendicular to 0y.

We'll take an unit of measure (for example, if you're working on a math sheet, a unit of measure could be the square from the page)

The negative values, on x axis, are on the left side of the origin and the positive values are on the right side. In the middle of the axis is origin, which has coordinates (0,0) where the two axes cross.

The positive values on the y axis are above the origin, and negative values are below origin.

For the point (-1,-11), we'll number 1 square on the left side of origin and we'll number 11 squares below origin.

Another way to draw the graph of the line is to calculate the x and y intercepts.

We'll put x = 0 for y intercept.

f(0) = 6

The resulted point has the coordinates: (0,6).

We'll put y = 0 for x intercept.

f(x) = 0

5x - 6 = 0

5x = 6

x = 6/5

The resulted point has the coordinates: (6/5,0).

ik9744 | Student

Since the previous answer already did the work out, but forgot to imply a graph, I made you one: 

echo "Some images are still being reviewed.