Write an equation in slope-intercept form of the line that passes through the given points.
1. (-3,4), (1,4)
2. (3, -2), (6,1)
2. (3,-2), (6,1)
The equation of the straight line passing through the points (x1, y1) and (x2, y2),
y - y1 = (y2 - y1)/(x2 - x1)* (x -x1)
y - -2 = (1 - -2)/(6 - -2)* (x - 3)
y + 2 = 3/8 (x - 3)
y = mx + b
y + 2 = 3/8 (x - 3)
solve for y
8y + 16 = 3(x -3)
8y + 16 = 3x - 9
y = 3/8x - 25/8
check my math
you try number 1
To find the equation in slope-intercept form of a line that passes through two points, we can use the slope-intercept form equation: y = mx + b. In this equation, m represents the slope of the line and b represents the y-intercept.
First, we need to find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two given points.
1. For the points (-3,4) and (1,4):
m = (4 - 4) / (1 - (-3)) = 0 / 4 = 0
Since the slope is 0, the equation becomes:
y = 0x + b
Next, we need to find the y-intercept (b). We can use one of the given points and substitute its coordinates (x, y) into the slope-intercept equation. Let's use the point (1, 4):
4 = 0(1) + b
4 = b
Therefore, the equation of the line becomes:
y = 0x + 4
y = 4
2. For the points (3, -2) and (6, 1):
m = (1 - (-2)) / (6 - 3) = 3 / 3 = 1
The slope is 1, so the equation becomes:
y = 1x + b
Using one of the given points, let's use (3, -2):
-2 = 1(3) + b
-2 = 3 + b
b = -5
Hence, the equation of the line is:
y = x - 5