Questions: 1) Write an equation to represent the relationship of x and y.
A) y = -2x
B) y = 2x
C) y = -2x + 1
D) y = 2x + 1
Transcript text: 1) Write an equation to represent the relationship of $x$ and $y$.
A) $y=-2 x$
B) $y=2 x$
C) $y=-2 x+1$
D) $y=2 x+1$
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Solution
△ Determine the equation of the line passing through given points.
○ Calculate slope
▷ Use two points to find the slope of the line.
☼ The slope \( m \) is \(-2\). Using points \((-1, 2)\) and \((0, 0)\), \( m = \frac{0 - 2}{0 - (-1)} = -2 \).
○ Determine y-intercept
▷ Identify where the line crosses the y-axis.
☼ The y-intercept is \( 0 \). The line crosses the y-axis at \((0, 0)\).
○ Formulate equation
▷ Use slope-intercept form to write the equation.
☼ The equation is \( y = -2x \). With \( m = -2 \) and \( b = 0 \), the equation is \( y = -2x + 0 \).
✧ The equation of the line is \( y = -2x \), corresponding to choice A.
☺
The equation of the line is $y = -2x$. This corresponds to answer choice A.