Mathematics, 29.01.2023 08:20, cheesecake1919

I need help with the problem .1. Find the Y-intercept of the following graph:2. What is the slope of the line?3. What is the Equation the line?

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answered: exoticbunnylover123

QUESTION 1

The y-intercept of a graph refers to the y-coordinate or value when the graph intersects the y-axis. This is the y-value at x = 0.

The graph in the problem has the y-coordinate as shown in the image below:

That point has a y-value of -2 by counting the boxes.

Therefore, the y-intercept is -2.

QUESTION 2

The slope of a line refers to the rate of change of the values in the y-axis to that in the x-axis. This can be written out mathematically as a formula to be:

$m=\frac{y_2-y_1}{x_2-x_1}$

We can pick two points on the graph as shown below:

The coordinates of these points 1 and 2 are:

$\begin{gathered} (x_1,y_1)=(-4,0) \\ (x_2,y_2)=(0,-2) \end{gathered}$

Using these coordinates, we can calculate the slope to be:

$\begin{gathered} m=\frac{-2-0}{0-\lbrack-4\rbrack}=\frac{-2}{4} \\ m=-\frac{1}{2} \end{gathered}$

The slope of the line is -¹/₂.

QUESTION 3

The equation of a straight line in the slope-intercept form is written out in the form:

$\begin{gathered} y=mx+b \\ \text{where } \\ x,y=\text{ variables} \\ m=\text{ slope} \\ b=y-\text{intercept} \end{gathered}$

In the previous questions, we have calculated the slope and y-intercept of the line to be:

$\begin{gathered} b=-2 \\ m=-\frac{1}{2} \end{gathered}$

Therefore, using these parameters, we have the equation of the line to be:

$\begin{gathered} y=-\frac{1}{2}x+(-2) \\ y=-\frac{1}{2}x-2 \end{gathered}$

The equation of the line is y = -¹/₂x - 2

I need help with the problem .1. Find the Y-intercept of the following graph:2. What is the slope of

answered: Guest

correct answer is option b.

step-by-step explanation:

the true statement about geometric figure is option b that is one line can be drawn through all three points.

if three points are on the same plane, they can be connected by a line.

answered: Guest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

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I need help with the problem .1. Find the Y-intercept of the following graph:2. What is the slope of...