Question

Write equations in slope-intercept form for three different lines that intersect at (-2,3). Show your work.

Answer 1

The equations of three lines intersecting at the point (-2,3) are calculated using different slopes and the point-slope form. The resulting equations in slope-intercept form are y = x + 5, y = -x + 1, and y = 2x + 7.

Step-by-step explanation:

The question requires us to write equations in slope-intercept form for three different lines that intersect at the point (-2,3). The slope-intercept form of an equation is y = mx + b, where m is the slope and b is the y-intercept. Since the lines must intersect at (-2,3), we can choose different slope values for each line and then calculate the corresponding y-intercepts.

Let's choose slopes 1, -1, and 2 for the three lines, respectively.

For the first line with slope 1:

1. Use the point-slope form to start: y - y1 = m(x - x1)
2. Plug in the point (-2,3) and m=1: y - 3 = 1(x + 2)
3. Simplify: y = x + 5

For the second line with slope -1:

1. Use point-slope form: y - y1 = m(x - x1)
2. Plug in the point and slope: y - 3 = -1(x + 2)
3. Simplify to slope-intercept form: y = -x + 1

For the third line with slope 2:

1. Use point-slope form: y - y1 = m(x - x1)
2. Apply the point and slope: y - 3 = 2(x + 2)
3. Simplify: y = 2x + 7

Therefore, the equations for the three lines in slope-intercept form are y = x + 5, y = -x + 1, and y = 2x + 7.