Question

Pls answerr RN I NEED IT RN 1:50 RN DUDE

Answer 1

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

`(\stackrel{x_1}{-8}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{5}-\stackrel{y1}{(-7)}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{(-8)}}} \implies \cfrac{5 +7}{4 +8} \implies \cfrac{ 12 }{ 12 } \implies 1`

`\begin{array} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{1}(x-\stackrel{x_1}{(-8)}) \implies y +7 = 1 ( x +8) \\\\\\ y+7=x+8\implies {\Large \begin{array}{llll} y=x+1 \end{array}}`

Answer 2

y = x + 1

Explanation:

let's take two points before finding the equation of line.

Points are (0,1) and (-1,0).

The equation of a line is a mathematical expression that describes the relationship between the x- and y-coordinates of any point on the line.

To find the equation of the line that passes through the points (0,1) and (-1,0), we can use the point-slope form of linear equations:

`\sf y - y_1 = m(x - x_1)`

where m is the slope of the line and (x1, y1) is one of the points on the line.

We can calculate the slope of the line using the following formula:

`\sf m = (y_2 - y_1)/(x_2 - x_1)`

where (x2, y2) is the other point on the line.

Substituting the coordinates of the points (0,1) and (-1,0) into the slope formula, we get:

`\sf m = (0 - 1)/(-1 - 0)=1`

Now that we know the slope of the line, we can use it to find the equation of the line using the point-slope form. Substituting the coordinates of the point (0,1) into the point-slope form, we get:

`\sf y - 1 = 1(x - 0)`

`\sf y - 1 = x`

Add 1 on both sides.

tex]\sf y - 1 + 1 = x+1 [/tex]

y = x + 1

Therefore, the equation of the line that passes through the points (0,1) and (-1,0) is:

y = x + 1