Graphing Equations Quick Check
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Question
Use the image to answer the question.
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 downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 1 right parenthesis and left parenthesis 1 comma negative 4 right parenthesis.
Write the equation of the line in slope-intercept form.
(1 point)
Responses
y=−5x−1
y equals negative 5 x minus 1
y=−5x+1
y equals negative 5 x plus 1
−5x−y=−1
negative 5 x minus y equals negative 1
y=5x+1
y equals 5 x plus 1
The correct answer is: y = -5x + 1
u r sure
Yes, I am sure. The equation y = -5x + 1 represents a line that passes through the points (0, 1) and (1, -4), as described in the question.
To write the equation of the line in slope-intercept form, we need to determine the slope (m) and the y-intercept (b).
Given that the line passes through the points (0,1) and (1,-4), we can calculate the slope as follows:
slope (m) = (change in y) / (change in x)
= (-4 - 1) / (1 - 0)
= -5 / 1
= -5
Now that we have the slope, we can use the point-slope form of the equation: y - y1 = m(x - x1), where (x1, y1) is one of the points on the line.
Using the point (0,1), we can substitute the values into the equation:
y - 1 = -5(x - 0)
Expanding and simplifying:
y - 1 = -5x + 0
y = -5x + 1
Therefore, the equation of the line in slope-intercept form is y = -5x + 1.