Question

Emma using a coordinate system to plan a rectangular monument. Side AB passes through point (2,0)

and is perpendicular to the graph of y = 1x – 3. Side CD is parallel to side AB and passes through
point (-1,6). What is the equation in slope-intercept form of the line that includes side CD?
I

Answer 1

The equation in slope-intercept form of the line that includes side CD is y = -x + 5.

Step-by-step explanation:

To find the equation of the line that includes the side CD, we first need to determine its slope.

1. The line AB is perpendicular to the graph of y = 1x - 3, which means its slope will be the negative reciprocal of the slope of y = 1x - 3.
2. The slope of y = 1x - 3 is 1, so the slope of side AB is -1/1 = -1.
3. Since side CD is parallel to side AB, it will have the same slope of -1.
4. Now that we have the slope, we can use the point-slope form of a line to find the equation of the side CD.
5. Using the point (-1,6) and the slope -1, we plug these values into the point-slope form:
6. y - y1 = m(x - x1)
7. So, y - 6 = -1(x - (-1))
8. Simplifying further, we get y - 6 = -1(x + 1)
9. Finally, we can rewrite this equation in slope-intercept form by solving for y:
10. y = -1(x + 1) + 6
11. This simplifies to y = -x - 1 + 6, and further to y = -x + 5.