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Questions

jimersonbaetaniebres @jimersonbaetaniebres

October 2022 1 7 Report

slope intercept form of the equation of the line

(-4,3) slope=1/4

(with solution)
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Answers & Comments

aaroncompaniados722

Answer:

$y = \frac{1}{4}x + 4 \ \textnormal{(Slope - Intercept Form: } y = mx + b \textnormal{)}\\\\\onehalfspacing\frac{1}{4}x - y = -4 \ \textnormal{(Standard Form: } ax + by = c \textnormal{)}$

Step-by-step explanation:

1.) Firstly, remember what the equation of a line is: $y = mx + b$ (for the equation of a line that is in slope-intercept structure), where $m$ is the slope, and $b$ is the y-intercept.

2.) To start, you understand what $m$ is; it's solely the slope, which you said was $\frac{1}{4}$ . So you can immediately fill in the condition for a line fairly to get: $y= \frac{1}{4}x + b$ .

⇒ $m = \frac{1}{4}$

⇒ $y = mx + b$ ⇒ $y= (\frac{1}{4})x + b$

3.) Next, what about $b$ , the y-intercept? To find $b$ , think about your $(x,y)$ point means: $(-4, 3)$ . When $x$ of the line is $-4$ , $y$ of the line must be $3$ . Since you said, the line passes through this point $(-4, 3)$ .

4.) Presently, have a look at our line's equation up until now. The value for $b$ is the thing that we need. The $\frac{1}{4}$ has kept now set, and $x$ and $y$ are only two "free variables" staying there. We can plug anything we need in for $x$ and $y$ here. However, we need the condition for the line that explicitly goes through the point $(-4, 3)$ .

5.) So, how about plugging in for $x$ the number $-4$ and for $y$ the number $3$ ? That will permit us to determine the value for $b$ for the specific line that goes through the point you gave.

⇒ $(x, y) = (-4, 3)$

⇒ $y = mx + b$

⇒ $3 = (\frac{1}{4})(-4) + b$

⇒ Solving for b: $3 = \frac{1 \times -4}{4} + b$

⇒ $3 = \frac{1 \times -4}{4} + b$

⇒ $3 = -1 + b$

⇒ $b = 3 - (-1) = 4$

⇒ $b = 4$

6.a.) Lastly, plug in or substitute the value of $m$ and $b$ back into the slope-intercept equation.

⇒ $y = mx + b$

⇒ $y = (\frac{1}{4})x + (4)$

⇒ $\bold{y = \frac{1}{4}x + 4}$ (Slope-Intercept Form)

6.b.) Unless you want the equation of the line in standard form, you may transpose the value of $b$ and the variable $y$ to the opposite sides of the equation.

⇒ $y = \frac{1}{4}x + 4$