Question

A. Determine the slope intercept equation of each line given two points on the line 1. (1, -3) and (-2, 6)

Answer 1

y = -3x

Step-by-step explanation

We have to determine the slope-intercept form of the equation of the line.

The slope-intercept form of a linear equation is given as:

y = mx + c

where m = slope

c = y intercept

First, we have to find the slope:

`m\text{ = }\frac{y2\text{ - y1}}{x2\text{ - x1}}`

where (x1, y1) and (x2, y2) are two points the line passes through.

Therefore:

`\begin{gathered} m\text{ = }(6-(-3))/(-2-1)=(6+3)/(-3)=(9)/(-3) \\ m=-3 \end{gathered}`

Now, we have to use the point-slope method to find the equation:

y - y1 = m(x - x1)

=> y - (-3) = -3(x - 1)

y + 3 = -3x + 3

y = -3x + 3 - 3

y = -3x

That is the slope intercept form of the equation.