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.
To find the equation of a line in slope-intercept form, we need two pieces of information: the slope (m) of the line and the y-intercept (b) of the line.
1. The line passes through (3,-3) and is parallel to the graph.
Since the line is parallel to another line, it means that they have the same slope. Start by finding the slope of the given graph or line.
Suppose the slope of the given line is m1. The line parallel to it will also have the slope m1.
Now we have the slope, m1, and one point on the line (3,-3). We can substitute these values into the slope-intercept form (y = mx + b) and solve for b:
-3 = m1 * 3 + b
b = -3 - m1 * 3
Therefore, the equation of the line passing through (3,-3) and parallel to the given graph is y = m1 * x + (-3 - m1 * 3).
2. The line passes through (2,-4) and is parallel to the graph of y = 2x - 5.
In this case, the given line has a slope of 2 (m1). Since the parallel line has the same slope, we can directly substitute the slope and the given point (2,-4) into the slope-intercept form:
y = m1 * x + b
-4 = 2 * 2 + b
b = -4 - 4
Therefore, the equation of the line passing through (2,-4) and parallel to the graph y = 2x - 5 is y = 2x + (-4 - 4).