Slope Problem

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Slope Problem Examples

Determine a value for x such that the line through the points has the given slope.

Let's use the slope formula and plug in what we know.

(x1,y1) (x2,y2)

4

30,5,2, mx

12

12

xx

yym

x

5

)2(0

4

3x

5

2

4

3

You can cross-multiply to find a fraction-free equation for x to solve.

2453 x

Example when you have a point and the slope

A point on a line and the slope of the line are given. Find two additional points on the line.

25,1 m

-1 0

Remember that slope is the change in y over the change in x. The slope is 2 which can be made into the fraction

1

2

(0,-3)

So this point is on the line also. You can see that this point is changing (adding) 2 to the y value of the given point and changing (adding) 1 to the x value.

+2+1To find another point on the line, repeat this process with your new point

(0,-3)+1 +2(1,-1) (-1,5)

y in

terc

ept

slop

e

Example of given an equation, find the slope and y intercept

Find the slope and y intercept of the given equation and graph it.

0443 yxFirst let's get this in slope-intercept form by solving for y. -3x +4 -3x +4

434 xy-4 -4

14

3 xy

bmxy

Now plot the y

intercept

From the y intercept,

count the slope

Change in y

Change in x

Now that you have 2 points you can draw

the line

Example of how to find x and y intercepts to graph a line

The x-intercept is where a line crosses the x axis

(6,0)

(-1,0)

(2,0)

What is the common thing you notice about the x-intercepts of these lines?

The y value of the point where they cross the axis will always be 0

To find the x-intercept when we have an equation then, we will want the y value to be zero.

Now let's see how to find the y-intercept

The y-intercept is where a line crosses the y axis

(0,4)

(0,1)

(0,5)

What is the common thing you notice about the y-intercepts of these lines?

The x value of the point where they cross the axis will always be 0

To find the y-intercept when we have an equation then, we will want the x value to be zero.

Let's look at the equation 2x – 3y = 12

Find the x-intercept. We'll do this by plugging 0 in for y

2x – 3(0) = 12 Now solve for x.

2x = 12

2 2x = 6 So the place where this line

crosses the x axis is (6, 0)

2x – 3y = 12

Find the y-intercept. We'll do this by plugging 0 in for x

2(0) – 3y = 12 Now solve for y.

-3y = 12

-3 -3

y = - 4 So the place where this line crosses the y axis is (0, -4)

We now have enough information to graph the line by joining up

these points

(6,0)

(0,- 4)