Write an equation in slope -intercept form of each line described. 1. slope 1/3 ; passes through (6,0) 2. slope 0; passes through (1,3) explain. !

The Slope intercept form of an linear equation is Y=mx+b
The 'm' in this equation is the slope
The 'b' is the Y intercept meaning when it touches the Y axis 
The Coordinate goes by (x,y) like alphabetically 
The 'Y' is the 'y' value and the 'X' is the 'x' value 
Question #1. Slope 1/3, passes (6,0) 
Step 1. Sub in the known variables. In this case you know the slope is 1/3 and the slope is the variable m. 
Y=mx+b
Y=1/3x+b
Step 2 sub in the coordinate to find the 'b' value or the 'y' intercept
(x,y)
(6,0)
Y=1/3x+b
0=(1/3)(6)+b
0=(6/3)+b
0=2+b
-2=b
Now you know that the slope is 1/3 and the 'b' or 'y' Intercept is -2
Step 3. Go back to the linear equation and sub in the variables you now know
Y=mx+b
Y=1/3x-2
Therefore the first equation in slope-intercept form is Y=1/3-2

The next question is a little bit trickier. The slope is 0. This means this is a horizontal line meaning it goes left to right. The equation for linear equations with a slope of '0' is Y=b. There is another special case. The other special case is when the slope is undefined. This means it is a vertical line going up and down.The equation of a line going up and down is X=b.

Step 1. Sub in the known variables. In this case you know the slope is 0
Y=0x+b
you know anything multiplied to '0' is '0' so you can just remove that from the equation.
Y=b
Step 2.sub in the coordinate to find the 'b' value or the 'y' intercept
Y=b
(x,y)
(1,3)
3=b 
Now you know what b so you put it in the equation for a horizontal line.
Y=3 is the equation of a slope of 0 and passes through (1,3)

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and y≤ -x +4 .

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

y≤ -x +4 .