How do you find the x and y intercept given $f (x) = \frac{2}{3} x + 4$ $f(x) = 2/3x + 4$ ?

Question

How do you find the x and y intercept given $f (x) = \frac{2}{3} x + 4$ $f(x) = 2/3x + 4$ ?

2 Answers

Impact of this question

2235 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-28T05:38:10

x-intercept: $= - 6$ $=-6$

y-intercept: $= 4$ $=4$

Explanation:

The given equation of straight line is

$f (x) = \frac{2}{3} x + 4$ $f(x)=2/3x+4$

$y = \frac{2}{3} x + 4$ $y=2/3x+4$

$- \frac{2}{3} x + y = 4$ $-2/3x+y=4$

$\frac{1}{4} (- \frac{2}{3} x + y) = 1$ $1/4(-2/3x+y)=1$

$- \frac{1}{6} x + \frac{y}{4} = 1$ $-1/6x+y/4=1$

$\frac{x}{- 6} + \frac{y}{4} = 1$ $x/{-6}+y/4=1$

Above equation is in standard intercept form: $\frac{x}{a} + \frac{y}{b} = 1$ $x/a+y/b=1$

which has

x-intercept: $a = - 6$ $a=-6$

y-intercept: $b = 4$ $b=4$

Answer 2 · 2018-07-28T06:20:14

The intercepts are $(- 6, 0)$ $(-6,0)$ on the $x$ $x$ -axis
and $(0, 4)$ $(0,4)$ on the $y$ $y$ -axis.

Explanation:

$f (x) = \frac{2}{3} x + 4$ $f(x) = 2/3x+4$ can be written as $y = \frac{2}{3} x + 4$ $y = 2/3x+4$

This is in slope-intercept form, $y = m x + c$ $y = mx +c$ so we immediately know that the $y$ $y$ -intercept is $4$ $4$ , the point $(0, 4)$ $(0,4)$
On the $y$ $y$ -axis the $x$ $x$ -value is always $0$ $0$ .

To find the $x$ $x$ - intercept, set $y = 0$ $y=0$ because on the $x$ $x$ -axis the $y$ $y$ -value is always $0$ $0$

$0 = \frac{2}{3} x + 4 \leftarrow \times 3$ $0=2/3x +4" "larr xx 3$

$0 = 2 x + 12$ $0 = 2x+12$

$- 12 = 2 x$ $-12 = 2x$

$- 6 = x \leftarrow$ $-6=x" "larr$ this is the $x$ $x$ -intercept

The two intercepts are $(- 6, 0) and (0, 4)$ $(-6,0) and (0,4)$

We could also have changed the original equation to :

$3 y = 2 x + 12$ $3y = 2x +12" "$ which is re-arranged to:

$2 x - 3 y = - 12 \leftarrow$ $2x-3y = -12" "larr$ this is standard form.

Set $x = 0$ $x =0$ to get $y = 4 \leftarrow$ $y = 4" "larr$ the $y$ $y$ -intercept

Set $y = 0$ $y=0$ to get $x = - 6 \leftarrow$ $x =-6" "larr$ the $x$ $x$ -intercept

Science

Math

Humanities

... and beyond

How do you find the x and y intercept given $f (x) = \frac{2}{3} x + 4$ $f(x) = 2/3x + 4$ ?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you find the x and y intercept given f(x)=23x+4f(x) = 2/3x + 4?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question

How do you find the x and y intercept given $f (x) = \frac{2}{3} x + 4$ $f(x) = 2/3x + 4$ ?