Question

PLEASE HELP ASAP

Answer 1

Step-by-step explanation:

1. We are given that slope is 4/3 and y-intercept is -3.

Now, the general form of a straight line is y = mx + c where m is the slope and c is the y-intercept.

So, in our case, the equation of the line is $y = \frac{4x}{3} -3$.

Now, substituting x=0 and y=0, we get the pair of points (x,y) = (0,-3) , ($\frac{9}{4}$,0).

So, plotting these points on a graph and joining them gives the required line as seen in graph 1 below.

We have, the slope intercept form of the line is $y = \frac{4x}{3} -3$.

2. We have the inequality 6x + 2y > 4.

In order to find the solution area, we will use the 'Zero Test' i.e. substitute x=0 and y=0. If the inequality is true, the shaded area is towards the origin and if its false, the shaded area is away from the origin.

Now, we have 6x + 2y > 4 → 0 > 4 which is false. So, the solution region is away from the origin as seen in the graph 2 below.

3. We have the equation 9x - 3y = 12.

A) The slope intercept form is y = 3x - 4.

Because, 9x - 3y = 12 →  3y = 9x - 12 → y = 3x - 4.

B) Now comparing y = 3x - 4 by the general form of a straight line, we see that slope of this line is 3 and y-intercept is -4.

C) We have to find the equation of line perpendicular to y = 3x - 4 having slope m_{1} = 3 and passing through ( 3,5 ).

As the lines are perpendicular, the slopes have the relation,

$m_{1} \times m_{2} = -1$

i.e. $3 \times m_{2} = -1$

i.e. $m_{2} = \frac{-1}{3}$

Now, using this slope $m_{2} = \frac{-1}{3}$ and the point ( 3,5 ) , we will find the equation of the line using the formula,

$(y - y_{1}) = m \times (x - x_{1})$

i.e. $(y - 5) = \frac{-1}{3} \times (x - 3)$

i.e. $3y - 15 = -x +3$

i.e. $x + 3y = 18$

So, the line perpendicular to y = 3x - 4 having slope m_{1} = 3 and passing through ( 3,5 ) is $x + 3y = 18$.

Answer 2

1)An equation in the slope-intercept form is written as

y=mx+by=mx+b

Where m is the slope of the line and b is the y-intercept. You can use this equation to write an equation if you know the slope and the y-intercept.

Example

Find the equation of the line

Choose two points that are on the line

Calculate the slope between the two points

m=y2−y1x2−x1=(−1)−33−(−3)=−46=−23m=y2−y1x2−x1=(−1)−33−(−3)=−46=−23

We can find the b-value, the y-intercept, by looking at the graph

b = 1

We've got a value for m and a value for b. This gives us the linear function

y=−23x+1y=−23x+1

In many cases the value of b is not as easily read. In those cases, or if you're uncertain whether the line actually crosses the y-axis in this particular point you can calculate b by solving the equation for b and then substituting x and y with one of your two points.

We can use the example above to illustrate this. We've got the two points (-3, 3) and (3, -1). From these two points we calculated the slope

m=−23m=−23

This gives us the equation

y=−23x+by=−23x+b

From this we can solve the equation for b

b=y+23xb=y+23x

And if we put in the values from our first point (-3, 3) we get

b=3+23⋅(−3)=3+(−2)=1b=3+23⋅(−3)=3+(−2)=1

If we put in this value for b in the equation we get

y=−23x+1y=−23x+1

which is the same equation as we got when we read the y-intercept from the graph.

To summarize how to write a linear equation using the slope-interception form you

Identify the slope, m. This can be done by calculating the slope between two known points of the line using the slope formula.Find the y-intercept. This can be done by substituting the slope and the coordinates of a point (x, y) on the line in the slope-intercept formula and then solve for b.

Once you've got both m and b you can just put them in the equation at their respective position.

https://www.mathplanet.com/education/algebra-1/formulating-linear-equations/writing-linear-equations.....

2)https://www.cymath.com/answer?q=6x%20%2B%202y%20%3E%204

3)https://www.cymath.com/answer?q=9x%20%E2%80%93%203y%20%3D%2012