87.1k views
4 votes
State the x-intercept, y intercept and the slope for each graph. Then write an equation in slope intercept form

State the x-intercept, y intercept and the slope for each graph. Then write an equation-example-1
User JDutton
by
7.9k points

1 Answer

10 votes

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

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

User Zacjordaan
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories