Question

write the slope intercept form of the equation (3,-4) and (-2,-4)

Answer 1

We know that a line is defined by two points. In this case, we need to find the line equation in the following form:

$y=mx+b$

We need to find the slope, m, and the y-intercept, b. To achieve this, we can use the two-point form of the line:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Now, we need to label those two points as follows:

• (3, -4) ---> x1 = 3, y1 = -4.

,

• (-2, -4) ---> x2 = -2, y2 = -4.

And we can substitute those values into the two-point form of the line:

$y-(-4)=\frac{-4-(-4)}{-2-3}(x-3)$

Solving the given operations:

$y+4=\frac{-4+4}{-5}(x-3)\Rightarrow y+4=\frac{0}{-5}(x-3)\Rightarrow y+4=0\cdot(x-3)$

Then

$y+4=0\Rightarrow y=-4$

If we need to write the equation in the slope-intercept form, we have that m = 0, and b = -4, then, the equation will be:

$y=0x+(-4)\Rightarrow y=0x-4$

In summary, the slope-intercept form of the equation is equal to y = 0x - 4:

$y=0x-4$

[We can notice that the line is parallel to the x-axis since the slope of the line is equal to 0, m = 0. The y-intercept (the point where the line passes through the y-axis) is equal to b = -4.]

A graph of the line is as follows: