Question

Write the slope intercept form (y=mx+b) for the equations of the lines that pass through Line 1: (0.8) (5,-4) Line 2: (-2.-6) (-4,6)​

Answer 1

To find the slope-intercept form for the given lines, calculate the slope from the provided points and use it along with one of the points to determine the y-intercept. The equations of Line 1 and Line 2 are y = (-12/5)x + 8 and y = -6x - 18 respectively.

Step-by-step explanation:

To determine the slope-intercept form of the equation for each line, we need to calculate the slope (m) for each pair of points and then use one of the points to find the y-intercept (b).

For Line 1 passing through points (0,8) and (5,-4):

• Calculate the slope (m):
  m = (y2 - y1) / (x2 - x1) = (-4 - 8) / (5 - 0) = -12 / 5
• Use the slope and one point to find the y-intercept (b): When x=0, y=8, thus b=8. Therefore, the equation is y = (-12/5)x + 8.

For Line 2 passing through points (-2,-6) and (-4,6):

• Calculate the slope (m):
  m = (6 - (-6)) / (-4 - (-2)) = 12 / (-2) = -6
• Use the slope and one point (for example, x=-2, y=-6) to find the y-intercept (b): -6 = (-6)(-2) + b, so b = -6 - 12 = -18. Therefore, the equation is y = -6x - 18.