Question

With slope –1/4, passing through (-4, -1)

Answer 1

Answer:

$y = -\frac{1}{4}x - 2$

Step-by-step explanation:

i'm not sure if you're trying to find the equation of the line ?? but i'll assume that's the case and find the slope-intercept form equation of the line.

slope intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. since the slope is already identified, you can plug in $-\frac{1}{4}$ for $m$.

• $y = mx + b$ ⇒ $y = -\frac{1}{4}x+b$

plug in the $x$ and $y$ values from the coordinate pair that passes through the line, which is (-4, -1). you can start with either $x$ or $y$, but i'm going to start with $x$.

first, plug in $-4$ for $x$.

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

now plug in $-1$ for $y$.

• $y = -\frac{1}{4}(-4)+b$ ⇒ $-1 = -\frac{1}{4}(-4)+b$

after plugging in all of the given values, the equation is now $-1 = -\frac{1}{4}(-4)+b$, in which you need to solve for $b$.

now it's time to solve! begin by multiplying $-\frac{1}{4}(-4)$ in order to simplify the right side of the equation.

• $-\frac{1}{4}(-4) = 1$

you now have $-1 = 1 + b$. subtract 1 from both sides of the equation. on the right side, it cancels itself out, leaving you with $b$. on the left side of the equation, you now have $-1 - 1$, which equals $-2$.

therefore $-2 = b$, or $b = -2$.

now that you've solved for your $b$ value, plug it into your initial slope-intercept form equation!

• $y = -\frac{1}{4}x + b$ ⇒ $y = -\frac{1}{4}x - 2$

if you want to check to make sure that the values are correct, plug (-4, -1) into your completed slope-intercept form equation. as you did in the beginning, plug in $-4$ for $x$ and $-1$ for $y$.

• $y = -\frac{1}{4}x - 2$ ⇒ $-1 = -\frac{1}{4}(-4) - 2$

begin simplifying by multiplying $-\frac{1}{4}(-4)$.

• $-1 = -\frac{1}{4}(-4) - 2$ ⇒ $-1 = 1 - 2$

subtract $1 - 2$.

• $-1 = 1 - 2$ ⇒ $-1 = -1$

since both sides of the equation are equal, that means your $b$ value of $-2$ is correct because it makes the equation true!

aaaand there you go! i hope this helps. have a great day! <3