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Sagot :
Answer:
B) y = 2x
Explanation:
We were given the following details:
The straight line passes through the origin; it passes through the point (0, 0)
The straight line passes through the point (1, 2)
[tex]\begin{gathered} (x_1,y_1)=(0,0) \\ (x_2,y_2)=(1,2) \end{gathered}[/tex]The general equation of a straight line is given by:
[tex]\begin{gathered} y=mx+b \\ where: \\ m=slope \\ b=y-intercept \end{gathered}[/tex]We will obtain the equation of the straight line as shown below:
I. Obtain the slope of the straight line
[tex]\begin{gathered} \begin{equation*} slope,m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1} \end{equation*} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{2-0}{1-0} \\ m=\frac{2}{1}=2 \\ m=2 \\ \\ \therefore slope,m=2 \end{gathered}[/tex]The slope of the straight line is 2
II. Obtain the y-intercept
Method 1:
The y-intercept refers to the point where the straight line crosses the y-axis.
In this case, the straight line crosses the y-axis at the origin (0, 0). This implies that:
[tex]\begin{gathered} b=0 \\ Remember:y=mx+b \\ \Rightarrow y=2x+0 \\ y=2x \end{gathered}[/tex]Method 2:
Using the point-slope equation:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-0=2(x-0) \\ y-0=2x-0 \\ y=2x \\ \\ \therefore y=2x \end{gathered}[/tex]Therefore, the answer is B (y = 2x)
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