Using the point-slope form of a linear equation, the equation of the line can be given as:
y - y₁ = m(x - x₁),
where (x₁, y₁) represents the point (1, -1) and m represents the slope, which is 3/2.
Substituting the values:
y - (-1) = (3/2)(x - 1).
Simplifying:
y + 1 = (3/2)(x - 1).
Now, we can rewrite the equation in slope-intercept form y = mx + b by solving for y:
y + 1 = (3/2)x - 3/2.
y = (3/2)x - 3/2 - 2/2.
y = (3/2)x - 5/2.
Therefore, the equation of the line is y = (3/2)x - 5/2.
To graph this line, plot the point (1, -1) on the coordinate plane and then use the slope (3/2) to find additional points. From the point (1, -1), you can go up 3 units and over 2 units to find the second point (3, 1), then go down 3 units and back 2 units to find the third point (-1, -4), and so on. Connect all the points to form a line. The graph should look like this:
Graph of the line with the given point (1, -1) and slope 3/2:
https://www.desmos.com/calculator/p8ft2zgkoh
Graph the line with the given point and slope.
The line through (1, -1) with slope 3/2.
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