Mathematics, 30.08.2019 21:30, jasminen3835232

Which line represents the direct variation equation y = 1/2 x?
line a
line b
line c
line d

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again, you need to remember that EVERY straight line has the equation

   y = (slope) x + (y-intercept) .

Right away, you know that this line goes through the origin ...
the equation doesn't show any y-intercept. The y-intercept is zero,
meaning that the line crosses the y-axis at the place where y=0.
That's the origin ... the place where the x- and y-axes cross.

Look at the graph they gave you. ... At first it looks like an ugly mess.
But look closer. There are only two lines there that go through the origin,
so one of those is the answer to the question.

Now let's talk about the slope of a line.

-- If the slope of a line is positive, that means it rises as it goes.
   If you walk the graph from left to right, you're climbing.

-- If the slope of a line is negative, that means it falls as it goes.
   If you walk the graph from left to right, you're going down-hill.

The equation they gave you is [ y = 1/2 x ].
The slope is 1/2 . That's positive.
The line on the graph slopes up. To walk it, you have to climb.

In the picture, that can only be line 'c' .

answered: Guest

to plot points for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4) in the parenthesis on the left of the comma is x and the right is y.

answered: Guest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is