Graphing Equations Practice
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Question
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An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows on both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 3 comma 0 right parenthesis.
Write the equation of the line in slope-intercept form.
(1 point)
To find the equation of the line in slope-intercept form, we first need to find the slope of the line. The slope is determined by the change in y divided by the change in x between the two points given.
Slope = (change in y)/(change in x)
Slope = (0 - (-2))/(3 - 0)
Slope = 2/3
Now that we have the slope, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Using the point (3, 0):
y - 0 = 2/3(x - 3)
Simplifying:
y = 2/3x - 2
Therefore, the equation of the line in slope-intercept form is y = 2/3x - 2.
wrong
Apologies for the incorrect response. Let's correct it.
Given the two points (0, -2) and (3, 0), we need to find the slope first to write the equation in slope-intercept form.
Slope (m) = (y2 - y1) / (x2 - x1)
Slope (m) = (0 - (-2)) / (3 - 0)
Slope (m) = 2 / 3
Now that we have the slope (m = 2/3) and one of the points (0, -2), we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
y - (-2) = (2/3)(x - 0)
y + 2 = (2/3)x
Finally, we rewrite the equation in slope-intercept form (y = mx + b) by isolating y:
y = (2/3)x - 2
Therefore, the correct equation of the line in slope-intercept form is y = (2/3)x - 2. Thank you for pointing out the error.