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What is the equation of the line? y=-(1)/(2)x-2 y=-2x-2 y=-(1)/(2)x-1 y=-2x-1

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What is the equation of the line? y=-(1)/(2)x-2 y=-2x-2 y=-(1)/(2)x-1 y=-2x-1

What is the equation of the line? y=-(1)/(2)x-2 y=-2x-2 y=-(1)/(2)x-1 y=-2x-1

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UlaProfessional · Tutor for 6 years

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To find the equation of the line, we can use the two points provided to calculate the slope and then use one of the points to find the y-intercept.Step 1: Calculate the slope (m) using the two points (-4, 0) and (0, -2).The slope formula is:\[m = \frac{y_2 - y_1}{x_2 - x_1}\]Using the points (-4, 0) as \((x_1, y_1)\) and (0, -2) as \((x_2, y_2)\), we get:\[m = \frac{-2 - 0}{0 - (-4)}\]\[m = \frac{-2}{4}\]\[m = -\frac{1}{2}\]Step 2: Use the slope and one of the points to find the y-intercept (b).The equation of a line is given by:\[y = mx + b\]We can use the point (0, -2) to find b because when x = 0, y is equal to the y-intercept. So, plugging in the values, we get:\[-2 = (-\frac{1}{2})(0) + b\]\[-2 = 0 + b\]\[b = -2\]Step 3: Write the equation of the line using the slope and y-intercept.\[y = mx + b\]\[y = -\frac{1}{2}x - 2\]Therefore, the correct equation of the line is:\[y = -\frac{1}{2}x - 2\]
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