Question

Through (5, -2), parallel to y=-3/4x-4

Answer 1

Answer:

1.75=b

Step-by-step explanation:

do the equation:

-2=3/4(5)+b

-2=-3.75+b

+3.75 to both sides

1.75=b

Answer 2

Answer:

$y=-\frac{3}{4}x+\frac{7}{4}$

Step-by-step explanation:

A line going through the point $(5,-2)$ and parallel to $y=-\frac{3}{4}x-4$.

• Let's first go over the parent linear equation, $y=mx+b$.

1. $y$ is your output value that one would see after inputting an $x$ value into an equation. In the case of the given point, $-2$ is our $y$ value.
2. $x$ is a variable that we put into an equation. In the case of the given point for this question, $5$ is our $x$ value.
3. $m$ is our slope for a linear equation. Slope can be represented as a fraction whose numerator is the rise or fall of your line, and the denominator is the run of your line.
4. $b$ is your $y$-intercept.

• If your function is parallel to $y=-\frac{3}{4}x-4$, then you already know that your slope is $m=-\frac{3}{4}$. Let's see how this impacts our parent function:

$y=mx+b\\y=-\frac{3}{4}x+b$

• Now, how do we find $b$? This is where the given line comes into play. If our line has to go through the point $(5,-2)$, then let's plug in these values for our $x$ and $y$, and solve for $b$.

$y=-\frac{3}{4}x+b\\-2=-\frac{3}{4}(5)+b\\ -2=-\frac{15}{4}+b\\-\frac{8}{4}+\frac{15}{4}=b\\ b=\frac{7}{4}$

• Our final equation is:

$y=-\frac{3}{4}x+\frac{7}{4}$