HELP THIS IS DUE TODAY 3. Han wanted to find the intercepts of the graph of the equation 10x + 4y = 20. He
decided to put the equation in slope-intercept form first. Here is his work
10x + 4y = 20
4y = 20 - 10x
y = 5 - 10x
He concluded that the x-intercept is (,0) and the v-intercept is (0.5).
a. What error did Han make?

b. What are the x- and y-intercepts of the line? Explain or show your reasoning.

Slope=

2.000

5.000

​

=2.500

x−intercept=−

5

10

​

=−2

y−intercept=

2

10

​

=5

Step-by-step explanation:

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

                    10*x-4*y-(-20)=0

STEP

1

:

Pulling out like terms

1.1     Pull out like factors :

  10x - 4y + 20  =   2 • (5x - 2y + 10)

Equation at the end of step

1

:

STEP

2

:

Equations which are never true

2.1      Solve :    2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Equation of a Straight Line

2.2     Solve   5x-2y+10  = 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  5x-2y+10  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 5/1 so this line "cuts" the y axis at y= 5.00000

 y-intercept = 10/2  =  5

Calculate the X-Intercept :

When y = 0 the value of x is -2/1 Our line therefore "cuts" the x axis at x=-2.00000

 x-intercept = -10/5  =  -2

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 5.000 and for x=2.000, the value of y is 10.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 10.000 - 5.000 = 5.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  5.000/2.000 =  2.500

Geometric figure: Straight Line

crown me pl

Step-by-step explanation:

if u dont mind

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be