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 write an equation in slope-intercept form, we need two pieces of information: the slope of the line and the y-intercept.
1. The line passes through (3, -3) and is parallel to the graph.
Since the line is parallel to the given graph, it will have the same slope. Therefore, we need to find the slope of the given graph.
Since the equation of the given graph is not given, we can rewrite it in slope-intercept form: y = 2x - 5.
From this equation, we can see that the slope of the given line is 2.
Now, we have the slope (m = 2) and a point (3, -3). We can use the point-slope form of a linear equation to find the equation of the parallel line.
Point-slope form: y - y1 = m(x - x1), where (x1, y1) is the given point.
Using the point (3, -3), we get: y - (-3) = 2(x - 3)
Simplifying: y + 3 = 2x - 6
To put the equation in slope-intercept form, we isolate y:
y = 2x - 6 - 3
y = 2x - 9
Therefore, the equation of the line parallel to the given graph and passing through (3, -3) is y = 2x - 9.
2. The line passes through (2, -4) and is parallel to the graph y = 2x - 5.
Again, since the line is parallel to the given graph, it will have the same slope.
From the given graph, we can see that the slope is 2.
Using the point-slope form with the given point (2, -4), we have: y - (-4) = 2(x - 2)
Simplifying: y + 4 = 2x - 4
To put the equation in slope-intercept form, we isolate y:
y = 2x - 4 - 4
y = 2x - 8
Therefore, the equation of the line parallel to the graph y = 2x - 5 and passing through (2, -4) is y = 2x - 8.