write an equation in the given form of the line passing through the given points.
A. slope-intercept form, passing through (-3, 4) and (1,4)
B. point-slope form, passing through (-3, 1) and slope 2.
A. To write the equation in slope-intercept form, we will use the formula:
y = mx + b
where m is the slope and b is the y-intercept.
First, we need to find the slope (m) of the line using the given points (-3, 4) and (1, 4). The formula to find the slope between two points (x1, y1) and (x2, y2) is:
m = (y2 - y1) / (x2 - x1)
Using the points (-3, 4) and (1, 4):
m = (4 - 4) / (1 - (-3))
m = 0 / 4
m = 0
The slope of the line passing through the given points is 0.
Now we can write the equation by substituting the values of m and one of the points (x, y) into the slope-intercept form:
y = mx + b
4 = 0 * (-3) + b
Since -3 * 0 = 0, the equation simplifies to:
4 = b
Therefore, the equation in slope-intercept form is:
y = 0x + 4
y = 4
B. To write the equation in point-slope form, we will use the formula:
y - y1 = m(x - x1)
where m is the given slope and (x1, y1) is the given point.
Using the point (-3, 1) and slope 2:
y - 1 = 2(x - (-3))
y - 1 = 2(x + 3)
y - 1 = 2x + 6
Therefore, the equation in point-slope form is:
y - 1 = 2x + 6