Graph the line with the given point and slope. Find two coordinates on a graph.
The line through (-2, 1) with slope 4/5.
To graph the line with the given point (-2, 1) and slope 4/5, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
The given slope is 4/5, so the equation of the line is y = (4/5)x + b.
To find the y-intercept, we can substitute the coordinates of the given point (-2, 1) into the equation and solve for b:
1 = (4/5)(-2) + b
1 = -8/5 + b
1 + 8/5 = b
13/5 = b
So the equation of the line is y = (4/5)x + 13/5.
To find two coordinates on the graph, we can choose two x-values and plug them into the equation to solve for the corresponding y-values.
Let's choose x = 0:
y = (4/5)(0) + 13/5
y = 0 + 13/5
y = 13/5
So when x = 0, y = 13/5, giving us the coordinate (0, 13/5).
Now let's choose x = 5:
y = (4/5)(5) + 13/5
y = 4 + 13/5
y = (20/5) + 13/5
y = 33/5
So when x = 5, y = 33/5, giving us the coordinate (5, 33/5).
Plotting the two coordinates on the graph, we get:
y-axis
|
|
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| (5, 33/5)
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|________________________x-axis
-2 0 5