Find the x and y intercepts for the following equation. 4x - 2y = 16

Mathematics

2 answers:

Aneli [31]3 years ago

6 0

The x is (4,0)
the y is (0,-8)

irinina [24]3 years ago

4 0

Answer:

( 4, 0 ) and ( 0,-8 )

Step-by-step explanation:

→ Rearrange into y = mx + c format

4x - 2y = 16

→ Minus 4x from both sides

-2y = -4x + 16

→ Divide everything by 2

-y = -2x + 8

→ Multiply everything by -1

y = 2x - 8

→ Substitute x = 0 to find the y-intercept and y = 0 to find the x intercept

x = 0 then y = -8 so ( 0,-8 )

y = 0 then x = 4 so ( 4, 0 )

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belka [17]

In the figure below

1) Using the theorem of similar triangles (ΔBXY and ΔBAC),

$\frac{BX}{BA}=\frac{BY}{BC}=\frac{XY}{AC}$

Where

$\begin{gathered} BX=4 \\ BA=5 \\ BY=6 \\ BC\text{ = x} \end{gathered}$

Thus,

$\begin{gathered} \frac{4}{5}=\frac{6}{x} \\ \text{cross}-\text{multiply} \\ 4\times x=6\times5 \\ 4x=30 \\ \text{divide both sides by the coefficient of x, which is 4} \\ \text{thus,} \\ \frac{4x}{4}=\frac{30}{4} \\ x=7.5 \end{gathered}$

thus, BC = 7.5

2) BX = 9, BA = 15, BY = 15, YC = y

In the above diagram,

$\begin{gathered} BC=BY+YC \\ \Rightarrow BC=15\text{ + y} \end{gathered}$

Thus, from the theorem of similar triangles,

$\begin{gathered} \frac{BX}{BA}=\frac{BY}{BC}=\frac{XY}{AC} \\ \frac{9}{15}=\frac{15}{15+y} \end{gathered}$

solving for y, we have

$\begin{gathered} \frac{9}{15}=\frac{15}{15+y} \\ \text{cross}-\text{multiply} \\ 9(15+y)=15(15) \\ \text{open brackets} \\ 135+9y=225 \\ \text{collect like terms} \\ 9y\text{ = 225}-135 \\ 9y=90 \\ \text{divide both sides by the coefficient of y, which is 9} \\ \text{thus,} \\ \frac{9y}{9}=\frac{90}{9} \\ \Rightarrow y=10 \end{gathered}$

thus, YC = 10.