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3 years ago

mrs.jackson gives the table below to her students in order for the function to be linear what must m be and why?

1 answer:

7 0

M or the slope has to be constant throughout the graph. This is because in order for a line to be linear it has to be increasing or decreasing at the same rate. So it the slope was 2 from point x 1 -2 then the slope changed to 1 from 3-4 it would not be linear. :)

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Step-by-step explanation:

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3 years ago

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maksim [4K]

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3 years ago

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What value of b will cause the system to have an infinite number of solutions?

irga5000 [103]

b must be equal to -6 for infinitely many solutions for system of equations $y = 6x + b$ and $-3 x+\frac{1}{2} y=-3$

<u>Solution: </u>

Need to calculate value of b so that given system of equations have an infinite number of solutions

$\begin{array}{l}{y=6 x+b} \\\\ {-3 x+\frac{1}{2} y=-3}\end{array}$

Let us bring the equations in same form for sake of simplicity in comparison

$\begin{array}{l}{y=6 x+b} \\\\ {\Rightarrow-6 x+y-b=0 \Rightarrow (1)} \\\\ {\Rightarrow-3 x+\frac{1}{2} y=-3} \\\\ {\Rightarrow -6 x+y=-6} \\\\ {\Rightarrow -6 x+y+6=0 \Rightarrow(2)}\end{array}$

Now we have two equations

$\begin{array}{l}{-6 x+y-b=0\Rightarrow(1)} \\\\ {-6 x+y+6=0\Rightarrow(2)}\end{array}$

Let us first see what is requirement for system of equations have an infinite number of solutions

If $a_{1} x+b_{1} y+c_{1}=0$ and $a_{2} x+b_{2} y+c_{2}=0$ are two equation

$\Rightarrow \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$ then the given system of equation has no infinitely many solutions.

In our case,

$\begin{array}{l}{a_{1}=-6, \mathrm{b}_{1}=1 \text { and } c_{1}=-\mathrm{b}} \\\\ {a_{2}=-6, \mathrm{b}_{2}=1 \text { and } c_{2}=6} \\\\ {\frac{a_{1}}{a_{2}}=\frac{-6}{-6}=1} \\\\ {\frac{b_{1}}{b_{2}}=\frac{1}{1}=1} \\\\ {\frac{c_{1}}{c_{2}}=\frac{-b}{6}}\end{array}$

As for infinitely many solutions $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

$\begin{array}{l}{\Rightarrow 1=1=\frac{-b}{6}} \\\\ {\Rightarrow6=-b} \\\\ {\Rightarrow b=-6}\end{array}$

Hence b must be equal to -6 for infinitely many solutions for system of equations $y = 6x + b$ and $-3 x+\frac{1}{2} y=-3$

8 0

3 years ago

Write the equation of a line that is parallel to {y=0.6x+3}y=0.6x+3y, equals, 0, point, 6, x, plus, 3 and that passes through th

Dominik [7]

y = 0.6x - 3.2
The general form of the desired equation is
y = mx + b
where
m = slope of the line
b = y intercept of the line
If two lines are parallel, their slopes will be the same, Since the slope of the
given line "y = 0.6x +3" is 0.6, that will also be the slope of the desired line.
So our equation becomes:
y = 0.6x + b
Now we can substitute the x and y value of the desired point we want the new line to pass through and find b. So
y = 0.6x + b
-5 = 0.6(-3) + b
-5 = -1.8 + b
-3.2 = b
So the desired equation is now
y = 0.6x - 3.2

3 0

3 years ago

mrs.jackson gives the table below to her students in order for the function to be linear what must m be and why?​

mrs.jackson gives the table below to her students in order for the function to be linear what must m be and why?