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3 years ago

Graph the line with slope - 1/3 and y-intercept -7.

Mathematics

1 answer:

Mnenie [13.5K]3 years ago

6 0

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

<em>m</em><em> - slope</em>

<em>b</em><em> - y-intercept (0, b)</em>

We have

$m=-\dfrac{1}{3},\ b=-7$

Substitute:

$y=-\dfrac{1}{3}x-7$

We only need two points to draw a line.

One we have: y-intercept → (0, -7).

Calculate other point:

Substitute <em>x = -3</em> to the equation of a line:

$y=-\dfrac{1}{3}(-3)-7=1-7=-6\to(-3,\ -6)$

Mark the points on the coordinate plane and draw a line through the given points.

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These are indeed quite a lot of exercises, but a lot of them are almost identical - only small computations will change. So, I'm glad to help you with one exercise from every cathegory, but I encourage you to solve the others on your own.

<h2>Exercise 1</h2>

You can call four consecutive integers as

$x,\ x+1,\ x+2,\ x+3$

So, the sum of the first and third is $x+(x+2) = 2x+2$

We want this quantity to be six less than the largest, i.e. $(x+3)-6 = x-3$

So, the equality is

$2x+2 = x-3$

Subtract x from both sides:

$x+2 = -3$

Subtract 2 from both sides:

$x = -5$

So, the consecutive integers are

$-5,\ -4,\ -3,\ -2$

In fact, the sum of the first and third is $-5-3 = -8$ , which is indeed six less than the largest: $-8 = -2-6$

<h2>Exercise 2</h2>

If you call the first odd number $x$ , the next consecutive odd numbers will be $x,\ x+2,\ x+4,\ x+6$

In fact, we have to count skipping two's, because we only want odd integers. From here, you go on like exercise 1: you write the largest (which is x+6), and set it to be two more than the sum of the other three (x, x+2 and x+4)

<h2>Exercise 3</h2>

By the same logic of exercise 2, two consecutive even integers are $x,\ x+2$ , assuming that x is even.

So, you set the equation as usual: the smaller (which is x) is 26 less than three times the larger (which means 3(x+2)-26)

<h2>Exercise 4 to 8</h2>

These are all pretty identical to exercise 1: you start by listing three or four consecutive integers:

$x,\ x+1,\ x+2\quad\text{or}\quad x,\ x+1,\ x+2\ x+3$

and then you translate the request of each exercise accordingly. Remember that expressions like "three times the second number" means that you have to multiply: $3(x+1)$ , while expression like "six more than the first" or "thirteen less than the first" imply adding/subtracting: $x+6$ or $x-13$ .