Graph the line with the given point and slope.
The line through (1, -1) with slope 3/5
To graph the line, we'll start at the given point (1, -1) and use the slope of 3/5 to find additional points on the line.
First, we'll find the y-intercept of the line using the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept. We can substitute the coordinates of the given point and solve for b:
-1 = (3/5)(1) + b
-1 = 3/5 + b
-1 - 3/5 = b
-5/5 - 3/5 = b
-8/5 = b
So the y-intercept is -8/5.
Now we can plot the given point (1, -1) and the y-intercept (0, -8/5) on a coordinate plane:
(y)
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Next, we'll find another point on the line by using the slope. The slope is 3/5, which can be written as a fraction (rise over run) or a decimal (0.6). If we move 5 units to the right (run) from the point (1, -1), we'll need to move 3 units up (rise) to find the next point.
Starting from (1, -1), we move 5 units to the right to get to (6, -1) and then 3 units up to get to (6, 2).
Now we have two points on the line: (1, -1) and (6, 2). We can connect these points to graph the line:
(y)
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*_____________________(x)
The line passes through the points (1, -1) and (6, 2).