What is the slope of the line y 5 − 4x?

Algebra Examples

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

y-5-(4*(x-2))=0

Step 1 :

Equation at the end of step 1 :

  (y - 5) -  4 • (x - 2)  = 0

Step 2 :

Equation at the end of step 2 :

  y - 4x + 3  = 0

Step 3 :

Equation of a Straight Line

3.1 Solve y-4x+3 = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line y-4x+3 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is -3/1 so this line "cuts" the y axis at y=-3.00000

  y-intercept = -3/1  = -3.00000

Calculate the X-Intercept :

When y = 0 the value of x is 3/4 Our line therefore "cuts" the x axis at x= 0.75000

  x-intercept = 3/4  =  0.75000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -3.000 and for x=2.000, the value of y is 5.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 5.000 - (-3.000) = 8.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

    Slope     =  8.000/2.000 =  4.000

Geometric figure: Straight Line

Slope = 8.000/2.000 = 4.000
x-intercept = 3/4 = 0.75000
y-intercept = -3/1 = -3.00000

Key Questions

#m# is the slope, while #b# is the y-intercept.
Any linear equation has the form of
#y=mx+b#
- #m# is the slope of the equation
- #b# is the y-intercept
The slope of the line, #m#, is found by
#m=(y_2-y_1)/(x_2-x_1)#
where #(x_1,y_1)# and #(x_2,y_2)# are the coordinates of any two points in the line.
The y-intercept, #b#, is found by plugging in #x=0# into the equation, which results in #y=b#, and therefore is the y-intercept.
In some cases, if the equation is already arranged for you nicely, like #y=3x+5#, we can easily find the y-intercept for this line, which is #5#.
Other times, the equation might not be arranged nicely, with cases such as #1/2x+3y=5#, in which we solve for the y-intercept:
#1/2x+3y=4#
#3y=4-1/2x#
#y=(-1/2x+4)/3#
#y=-1/6x+4/3#

So, the y-intercept of this line is #4/3#.
The #y#-intercept #b# can be found by reading the #y#-axis where the graph hits the y-axis, and the slope #m# can be found by finding any two distinct points #(x_1,y_1)# and #(x_2,y_2)# on the graph, and using the slope formula below.
#m={y_2-y_1}/{x_2-x_1}#.
I hope that this was helpful.
#y = mx + b#
Where:
#m# is the slope of the line.
#b# is the y-intercept of the line.
Consider #y = x#
graph{y=x [-10, 10, -5, 5]}
In this equation, the coefficient to #x# is 1 and our y-intercept is 0.
We could think of that equation as looking like:
#y = 1x + 0#
Notice that the graphed line has a "rise-over-run" of #1/1# which is just 1 and the line passing through the y-axis at #y=0#