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

## Answers

Answer:1.75=bStep-by-step explanation:do the equation:-2=3/4(5)+b-2=-3.75+b+3.75 to both sides1.75=b

Answer:[tex]y=-\frac{3}{4}x+\frac{7}{4}[/tex]Step-by-step explanation:A line going through the point [tex](5,-2)[/tex] and parallel to [tex]y=-\frac{3}{4}x-4[/tex].Let's first go over the parent linear equation, [tex]y=mx+b[/tex].[tex]y[/tex] is your output value that one would see after inputting an [tex]x[/tex] value into an equation. In the case of the given point, [tex]-2[/tex] is our [tex]y[/tex] value.[tex]x[/tex] is a variable that we put into an equation. In the case of the given point for this question, [tex]5[/tex] is our [tex]x[/tex] value.[tex]m[/tex] 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.[tex]b[/tex] is your [tex]y[/tex]-intercept.If your function is parallel to [tex]y=-\frac{3}{4}x-4[/tex], then you already know that your slope is [tex]m=-\frac{3}{4}[/tex]. Let's see how this impacts our parent function:[tex]y=mx+b\\y=-\frac{3}{4}x+b[/tex]Now, how do we find [tex]b[/tex]? This is where the given line comes into play. If our line has to go through the point [tex](5,-2)[/tex], then let's plug in these values for our [tex]x[/tex] and [tex]y[/tex], and solve for [tex]b[/tex].[tex]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}[/tex]Our final equation is:[tex]y=-\frac{3}{4}x+\frac{7}{4}[/tex]