Question

Find the equation of the line passingthrough the points (3,-2) and (4, 6).y = [? ]x + 1

Answer 1

To answer this question, we can use the two-point equation of the line as follows:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Now, we need to identify the points in order to apply the previous formula:

(3, -2) ---> x1 = 3, y1 = -2

(4, 6) ---> x2 = 4, y2 = 6

Then, we have:

`y-(-2)=(6-(-2))/(4-3)(x-3)`
`y+2=(6+2)/(4-3)(x-3)=y+2=(8)/(1)(x-3)`
`y+2=8(x-3)=8x-24`

We applied the distributive property on the right side of the equation.

Finally, we have:

`y+2=8x-24\Rightarrow y=8x-24-2\Rightarrow y=8x-26`

Therefore, the line equation in the slope-intercept form is:

`y=8x-26`