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2 years ago

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Mathematics

1 answer:

forsale [732]2 years ago

6 0

Answer:

y=-1/3x-8

Step-by-step explanation:

Here is the equation for slope-intercept form: y=mx+b

Ok first, let's find the y intercept, which is equal to b in slope-intercept form.

To find the y intercept, we need to look at the y axis. It is the point where the line touches it. The graph shows that the line touches the y axis at -8, so that is the y intercept, (0, -8).

Now, from that point, we need to find the slope, which is equal to m in slope-intercept form.

To find the slope, start on the point that you are on, which should be the y intercept, and count how many spaces you need to go up or down, and then left or right until you get to any other point on the line. These are called the rise (change in y) and run (change in x) respectively. The slope is equal to the rise over the run, or rise/run.

In this case, we can choose any point on the line that is shown on the graph that isn't the y intercept. I'll chose the point on the right nearest to the y intercept. From the point we are on, which is (-8,0), we will need to move one space down and three to the right.

One space down on the y axis is -1, and three spaces to the right on the x axis is +3, so our slope will be -1/+3, which is -1/3.

Let's go back to the slope-intercept form. y=mx+b. Now we can plug our information in.

We know the y intercept is -8, which is b,

and we know the slope is -1/3, which is m.

So substituting for b and m, we get y=-1/3x-8.

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Sketch a system of linear equations that has a solution of (-3, 7) on the coordinate grid provided. WILL GIVE BRAINIEST

ludmilkaskok [199]

Answer:

y=x+10

y=-2x+1

(see attached picture)

Step-by-step explanation:

The idea of solving a system of equations graphically is taht both graphs cross each other at the same point.

The problem doesn't state so, but we can find the equations of the lines that pass through the desired point by using the point-slope form of the equation and by picking any slope we wish.

The slope-intercept form of a linear equation looks like this:

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

so let's use the following slopes: $m_{1}=1$ and $m_{2}=-2$ . Remember, you can pick any slope you wish.

so now we can substitute the provided point (-3,7) and its respective slopes:

$m_{1}=1$

y-7=1(x-(-3))

y=x+3+7

y=x+10

this will be our first equation.

$m_{2}=-2$

y-7=-2(x+3)

y=-2x-6+7

y=-2x+1

so now we can plot the graphs of the given equations.

how to plot them? you can pick any x-value you like and use the provided equatioins to find the corresponding y-value. You plot the two points and build the graph.

Let's take the first equation:

y=x+10

and let's use the x-value x=0. We now substitute that into the equation so we get:

y=0+10

y=10

so now my two ordered pairs are (0,10) and (-3,7) so I can plot them on my graph and connect them with a straight line. (see attached picture.)

and we can follow the same procedure for the second graph.

let's use the x=0 again so we get:

y=-2(0)+1

y=1

so the ordered pairs are: (0,1) and (-3,7)

so we plot them to get our final graph (see attached picture)

Of course, this is one of the ways in which we can solve this problem. Since they are asking us to plot the graphs and not quite finding the equations for the system of equations, you could just draw any two lines you like and the answer would be correct as long as the two lines pass through the same point.