What are the slope and the y-intercept of the graph of the equation y = -4x - 5?

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What are the slope and the y-intercept of the graph of the equation y = -4x - 5?

C) The y-intercept is the same for both

D) The graph and the equation expression an equivalent function.

Step-by-step explanation:

We are given graph a linear function and a equation of line y = -4x - 4

From the given graph, let's find the equation.

From the graph, we know the slope = rise/run

Here rise = 4 and run -1

Slope = 4/-1 = -4

and

y-intercept is -4 (where the line cuts the y-axis)

The equation of graph of the line y = -4x - 4

So, the graph and the given equation are also the same.

Therefore, the answers are

C) The y-intercept is the same for both

D) The graph and the equation expression an equivalent function.

I hope my answers are correct. If they are, please do brainliest. Thanks.

y-intercept is (0, -5)

slope is -4

Step-by-step explanation:

I used Desmos to graph the equation and find the y-intercept.

Slope = (y2 - y1) / (x2 - x1)

2 points: (-1.25, 0) and (0, -5)

(-5 - 0) / (0 - - 1.25)

-5 / (0 + 1.25)

-5 / 1.25

= -4

[tex]What are the slope and the y-intercept of the graph of the equation y = -4x - 5?[/tex]

see the explanation

Step-by-step explanation:

we know that

The linear equation in slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

Part 1) we have

[tex]y=-4x-6[/tex]

This is the equation of a line in slope intercept form

therefore

The slope is m=-4

The t-intercept is b=-6

see the attached figure to better understand the problem

Part 2) we have

[tex]y=-\frac{1}{2}x-\frac{1}{3}[/tex]

This is the equation of a line in slope intercept form

therefore

The slope is m=-1/2

The t-intercept is b=-1/3

see the attached figure to better understand the problem

[tex]Find the slope and the y-intercept of the graph of the linear equation. 1. y = -4x - 6 2. y = 1/2x -[/tex]

ANSWER TO QUESTION 1

The equation of a line in slope intercept form is given by the formula,

[tex]y = mx + c[/tex]

where

[tex]m[/tex]

is the slope of the straight line and

[tex]c[/tex]

is the y-value of the y-intercept.

It was given in the question that, the slope is -4.

Thus,

[tex]m = - 4[/tex]

It was also given that the y-intercept is -3.

Thus,

[tex]c = - 3[/tex]

Therefore the equation is

[tex]y = - 4x + - 3[/tex]

This gives us,

[tex]y = - 4x - 3[/tex]

The correct answer is A

ANSWER TO QUESTION 2

We were given that the equation passes through the two points (-2,1) and (2,1).

We can see from the points that the y-values are constant. This means that the line is parallel to the x-axis

Therefore the equation is given by

[tex]y=y_1[/tex]

where

[tex]y_1[/tex]

is the constant y-value.

Thus, the equation is,

[tex]y = 1[/tex]

or we write in general form to get,

[tex]y - 1 = 0[/tex]

The correct answer is A.

We could have also decided to find the slope,

[tex]m = \frac{ 1 - 1}{2 - - 2} = \frac{0}{4} = 0[/tex]

using any point, say

[tex](2,1)[/tex]

we plug into the point slope form formula to get,

[tex]y - 1 = 0(x - - 2)[/tex]

This gives us

[tex]y - 1 = 0[/tex]

ANSWER TO QUESTION 3

The equation of a straight line in the slope intercept form is

[tex]y = mx + c[/tex]

where m is the slope and c is the y-intercept.

Thus,

[tex]m = - \frac{1}{3}[/tex]

and

[tex]c = \frac{10}{3}[/tex]

We substitute in to the formula to obtain,

[tex]y = - \frac{1}{3} x + \frac{10}{3}[/tex]

we multiply through by 3 to obtain,

[tex]3y = - x + 10[/tex]

We rewrite in general form by equating everything to zero.

Thus,

[tex]3y + x - 10 = 0[/tex]

Or

[tex]x + 3y - 10 = 0[/tex]

The correct answer is option D.

ANSWER TO QUESTION 4

We want to write the equation of the line that has an x-intercept of -3 and passes through the point (-3, 7).

This implies that the line passes through the points,

[tex](-3,0) \: and \: (-3,7)[/tex]

We find the slope as follows,

[tex]m = \frac{7 - 0}{ - 3 - - 3} = \frac{7 - 0}{ - 3 + 3}[/tex]

This implies that,

[tex]m= \frac{7}{0}[/tex]

The slope is undefined. This means the line is parallel to the y-axis.

The equation of a line that has an undefined slope or parallel to the y-axis is given by

[tex]x=x_1[/tex]

where

[tex]x_1 = - 3[/tex]

Therefore the equation is

[tex]x = - 3[/tex]

The correct answer is A.

or you could have also obtained the equation as follows using any of the points.

[tex]y - 7 = \frac{7}{0} (x + 3)[/tex]

This implies that,

[tex]0(y - 7) = 7(x + 3)[/tex]

[tex]0 = 7(x + 3)[/tex]

We divide through by 7 to get,

[tex]0 = x + 3[/tex]

hence

[tex]x = - 3[/tex]

(3) The y-intercept is the same for both.

(4) The graph and the equation express an equivalent

function.

Step-by-step explanation:

The slope of both functions is negative since in the graph the line is going down, then the Y intercept is the same for both because when X is 0, in the graph the line is located at Y=-4 and in the function you can set x to 0 and the function would be -4, then you can see that the function and the graph have the same slope and the same Y intercept that means that they express an equivalent function.

In y = mx + b form, the slope is in the m position and the y int is in the b position

1. slope of -4y int of -3

y = -4x - 3 <==

2. (-2,1)(2,1)...u have the same y coordinates..this means u have a horizontal line with a slope of 0.

y = 1y - 1 = 0 <===

3. slope = -1/3 and y int = 10/3...

y = -1/3x + 10/3add 1/3 to both sides

1/3x + y = 10/3...multiply everything by 3

x + 3y = 10

x + 3y - 10 = 0 <==

4. (-3,7)...and if the x int is -3, then its points are (-3,y)...meaning u have points where the x coordinates are the same...meaning vertical lines...ur answer is x = -3