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]
[tex]y=-\frac{3}{4}x+\frac{7}{4}[/tex]
