Which equation in slope-intercept form represents a line that is parallel to y=−4x−5 and passes through the point (0,0)?
A: y=−4x−7
B: y=4x−7
C: y=4x−9
D: y=−1/4x−5
E: y=−4x
y=-4x
well, the slope is -4
and the y-intercept is 0
so, ...
To find the equation of a line that is parallel to y = -4x - 5 and passes through the point (0,0), we need to use the same slope as the given line.
The equation y = mx + b is in slope-intercept form, where m is the slope and b is the y-intercept. Since we know that the line is parallel to y = -4x - 5, the slope will be -4.
Now we can substitute the slope (-4) and the point (0,0) into the equation and solve for b:
0 = -4(0) + b
0 = 0 + b
b = 0
Therefore, the equation for the line that is parallel to y = -4x - 5 and passes through the point (0,0) is y = -4x.
So the correct answer is E: y = -4x.
To find the equation of a line that is parallel to the line y = -4x - 5 and passes through the point (0,0), we need to consider the following:
1. The slope of the parallel line will be the same as the slope of the given line, which is -4.
2. We can use the point-slope form of the equation of a line: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Using these two facts, we can find the equation of the line. Plugging in the values, we get:
y - 0 = -4(x - 0)
Simplifying, we get:
y = -4x
Comparing this equation to the answer choices, we can see that option E: y = -4x represents the equation of a line that is parallel to the given line and passes through the point (0,0). Therefore, the correct answer is E: y = -4x.