Write an equation in slope-intercept form for each described line.
1.The line passes through (3,-3)and is parallel to the graph.
2.The line passes through (2,-4) and is parallel to the graph of y=2x-5.
3.The line passes through the orgin with slope 2
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3
1. what graph?
2. since parallel , it must be
y = 2x + b
sub in the point (2,-4) to find b
3. y = (2/3)x
To write an equation in slope-intercept form for each line, we need to use the slope-intercept form equation: y = mx + b, where m is the slope of the line and b is the y-intercept.
1. The line passes through (3, -3) and is parallel to the graph.
To find the slope (m) of the line, we need to know that parallel lines have the same slope. Since we don't have the equation of the given graph, we cannot determine the slope directly. However, knowing that parallel lines have the same slope, we can assume that the slope of the given line will be the same as the unknown graph.
Given the point (3, -3), we can substitute the values of x and y into the equation to solve for b:
-3 = m(3) + b
Since we do not know the value of m, we cannot determine b directly. Therefore, the equation for the line parallel to the graph passing through (3, -3) in slope-intercept form will be:
y = mx + b
2. The line passes through (2, -4) and is parallel to the graph of y = 2x - 5.
In this case, we already have the equation of the given graph: y = 2x - 5. Since the line we are looking for is parallel to this line, it will have the same slope (m = 2).
Given the point (2, -4), we can substitute the values of x and y into the equation to solve for b:
-4 = 2(2) + b
-4 = 4 + b
b = -8
Therefore, the equation for the line parallel to the graph y = 2x - 5 passing through (2, -4) in slope-intercept form will be:
y = 2x - 8
3. The line passes through the origin with a slope of 2/3.
Given the information that the line passes through the origin (0, 0) with a slope of 2/3 (m = 2/3), we can directly substitute these values into the slope-intercept form equation to solve for b:
0 = (2/3)(0) + b
0 = 0 + b
b = 0
Therefore, the equation for the line passing through the origin with a slope of 2/3 in slope-intercept form will be:
y = (2/3)x + 0
y = (2/3)x