In $y=5x+6$, is the $6$ the $y$-intercept or the $x$-intercept?

woowheedr
2022-07-03
Answered

In $y=5x+6$, is the $6$ the $y$-intercept or the $x$-intercept?

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asked 2022-09-24

Let $L$ be the tangent line to $y=\mathrm{tan}(2x)$ at $(\frac{\pi}{2},0)$. What is the $y$-intercept of $L$?

(a) $\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}0\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}$

(b) $\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\frac{\pi}{2}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}$

(c) $\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}-\pi \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}$

(d) $\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}1\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}$

(e) $\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}2\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}$

(a) $\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}0\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}$

(b) $\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\frac{\pi}{2}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}$

(c) $\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}-\pi \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}$

(d) $\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}1\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}$

(e) $\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}2\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}$

asked 2022-06-27

Function: $f(x)=\frac{\mathrm{sin}(x)}{x}$. Why is the $y$-intercept $=1$ despite $\mathrm{sin}(0)$ being divided by zero?

asked 2022-04-06

Let $f(x)={x}^{2}+x-6$.

a. Write down the $y$-intercept of the graph of $f$.

how do we figure this out? I know $f(x)$ means $y$, so do we use the quadratic formula? ${x}^{2}+x-6$.

b. Solve $f(x)=0$.

We plug $0$ into the $x$’s in the original formula, right?

a. Write down the $y$-intercept of the graph of $f$.

how do we figure this out? I know $f(x)$ means $y$, so do we use the quadratic formula? ${x}^{2}+x-6$.

b. Solve $f(x)=0$.

We plug $0$ into the $x$’s in the original formula, right?

asked 2022-05-09

The gradient is $m=-4/3$, and the point given is $(3/2,3)$

Let $c$ be the $y$-intercept

$y=mx+c$

$y=(-4/3)x+c$

If I substitute $x$ and $y$ from the point given, $3=(-4/3)(3/2)+c$ and look for $c$, I get $c=5$

But according to my answer sheet, $c=33/8$ by using $y-{y}_{1}=m(x-{x}_{1})$

Why are the two methods giving different answers?

Let $c$ be the $y$-intercept

$y=mx+c$

$y=(-4/3)x+c$

If I substitute $x$ and $y$ from the point given, $3=(-4/3)(3/2)+c$ and look for $c$, I get $c=5$

But according to my answer sheet, $c=33/8$ by using $y-{y}_{1}=m(x-{x}_{1})$

Why are the two methods giving different answers?

asked 2022-08-31

Solve. m=3, b=1

asked 2022-07-01

How to prove that $\frac{x}{a}}+{\displaystyle \frac{y}{b}}=1\phantom{\rule{thickmathspace}{0ex}$ where $\phantom{\rule{thinmathspace}{0ex}}a$ is the $\phantom{\rule{thinmathspace}{0ex}}x$-intercept and $\phantom{\rule{thinmathspace}{0ex}}b$ is the $\phantom{\rule{thinmathspace}{0ex}}y$-intercept for all $\phantom{\rule{thinmathspace}{0ex}}a,b\ne 0$

asked 2022-07-23

Let say in x,y dimension if a line cross over the x-axis instead of y (as shown in image above, unlike y=mx+c ) then how equation will change or will the equation has any impact apart from the x-intercept in this case? Is this a valid case?