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State the x-intercept, y intercept and the slope for each graph. Then write an equation in slope intercept form

State The Xintercept Y Intercept And The Slope For Each Graph Then Write An Equation In Slope Intercept Form class=

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Answer:

1.

x-intercept = 8/5

y-intercept = -4

m = 1.5 (or 5/2)

equation: y = 1.5x - 4

2.

x-intercept = -1/2

y-intercept = -3

m = -6

equation: y = -6x - 3

Useful things to note:

Definition of a y-intercept: The y value when x = 0.

Definition of a x-intercept: The x value when y = 0.

Definition of the slope-intercept form: y = mx + b

  • b = the y-intercept

Step-by-step explanation:

1.

We don't know the x-intercept yet, but we can easily find the y-intercept.

So on the x = 0 line, we see there's a point right at (0, -4). So, the y-intercept is at -4.

The other point that's given is (2, 1). This is useful for getting the slope-intercept form.

y = mx + b

Lets solve for m.

When solving for m in the slope-intercept form, we replace x and y with an available point. For this we'll use (2, 1). We already know that b = the y-intercept, which is -4. Combining these two facts, we get this equation:

1 = 2m - 4

Let's solve this:

1 = 2m - 4

1 + 4 = 2m -4 + 4

5 = 2m

5/2 = 2m/2

1 1/2 = m

or

1.5 = m

Now that we have m, we can easily get the equation!

b = -4

m = 1.5

replacing those in the slope-intercept formula, we get:

y = mx + b

y = (1.5)x + (-4)

equation: y = 1.5x - 4

in order to finally find the x-intercept, we find where x is when y = 0. (I'm going to use m = 5/2 for easiest convenience. All of those values work though :) )

y = 5/2x - 4

make y = 0

0 = 5/2x - 4

0 + 4 = 5/2x - 4 + 4

4  = 5/2x

4*(2/1)  = 5/2x*(2/1)

8 = 5x

8/5 = 5x/5

8/5 = x

2.

We don't know the x-intercept yet, but we can easily find the y-intercept.

So on the x = 0 line, we see there's a point right at (0, -3). So, the y-intercept is at -3.

The other point that's given is (-1, 3). This is useful for getting the slope-intercept form.

y = mx + b

Lets solve for m.

When solving for m in the slope-intercept form, we replace x and y with an available point. For this we'll use (-1, 3). We already know that b = the y-intercept, which is -3. Combining these two facts, we get this equation:

3 = -1m - 3

Let's solve this:

3 = -1m - 3

3 + 3 = -1m -3 + 3

6 = -1m

6/-1 = -1m/-1

-6 = m

or

-6 = m

Now that we have m, we can easily get the equation!

b = -3

m = -6

replacing those in the slope-intercept formula, we get:

y = mx + b

y = (-6)x + (-3)

equation: y = -6x - 3

in order to finally find the x-intercept, we find where x is when y = 0.

y = -6x - 3

make y = 0

0 = -6x - 3

0 + 3 = -6x - 3 + 3

3 = -6x

3/(-6) = -6x/(-6)

-3/6 = x

simplify

-1/2  = x

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