Find the equation for a line which passes through the points (–1, 1) and (3, –7). Write the
equation in slope-intercept form. Show work.
To find the equation of a line passing through two points, you need to determine the slope and the y-intercept of the line.
Step 1: Calculate the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Let's use the two given points: (-1, 1) and (3, -7)
m = (-7 - 1) / (3 - (-1))
= (-8) / (4)
= -2
Step 2: Once you have the slope, you can use the point-slope form of the equation which is:
y - y1 = m(x - x1)
Using the point (-1, 1), the equation becomes:
y - 1 = -2(x - (-1))
y - 1 = -2(x + 1)
y - 1 = -2x - 2
Step 3: Convert the equation to slope-intercept form (y = mx + b) by isolating y:
y = -2x - 2 + 1
y = -2x - 1
Therefore, the equation of the line passing through the points (-1, 1) and (3, -7) is y = -2x - 1 in slope-intercept form.