Question

Graph the line with the given point and slope.
The line through ​(1​, -1​) with slope 3/2.

Answer 1

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