Respuesta :
Answer:
b
Step-by-step explanation:
The equation of a line passing through the origin is
y = mx ( m is the slope )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0 ) and (x₂, y₂ ) = (3, 4 )
m = [tex]\frac{4-0}{3-0}[/tex] = [tex]\frac{4}{3}[/tex]
y = [tex]\frac{4}{3}[/tex] x → b
The equation of the line though (0, 0) and (3, 4) is [tex]y=\frac{4}{3}x[/tex]
The correct answer is an option (b)
What is the formula for the equation of line passing through two points?
"If the line is passing through points [tex](x_1,y_1),(x_2,y_2)[/tex] then the formula to find the equation of line is [tex]\frac{y-y_1}{y_2-y_1}= \frac{x-x_1}{x_2-x_1}[/tex]"
For given question,
The line passes though points (0, 0) and (3, 4)
Let [tex](x_1,y_1)=(0,0),(x_2,y_2)=(3,4)[/tex]
Using two-point form of line,
[tex]\Rightarrow \frac{y-y_1}{y_2-y_1}= \frac{x-x_1}{x_2-x_1} \\\\\Rightarrow \frac{y-0}{4-0}= \frac{x-0}{3-0}\\\\ \Rightarrow \frac{y}{4} =\frac{x}{3}\\\\ \Rightarrow y=\frac{4}{3} x[/tex]
Therefore, the equation of the line though (0, 0) and (3, 4) is [tex]y=\frac{4}{3}x[/tex]
The correct answer is an option (b)
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