If the graph of the equation `y=5x+3` is shifted down 4 units, what is the x-intercept of the new line?

Options

A. `-1`
B. `(1)/(5)`
C. `1`
D. `(5)/(4)`

Answer

B

Explanation

Difficult: Medium
Category: Heart of Algebra/ Linear Equations
Strategic Advice: You aren't given a graph to shift, so either draw a quick sketch of the given line or mentally picture what happens when the line is shifted. Don't forget- When a linear equation is written in the form `y=mx+b`, m is the slope of the line and b is the y-intercept (not the x-intecept).
Getting to the Answer: The graph of the given line has a slope, but the intercept moves down 4, so the new y-interscept is `3-4=-1` . Wait, though choice A is not the correct answer. The question asks for the x-intercept of the new line, not the y-intercept. The equation of the line is `y=5x-1`. Set `y=0` and solve for x:
`0=5x-1`
`1=5x`
`x=(1)/(5)`
This means (B) is correct.