Question

What is an equation of the line that passes through the points left bracket, minus, 3, comma, 1, right bracket(−3,1) and left bracket, minus, 4, comma, 0, right bracket(−4,0)?

Answer 1

The equation of the line passing through the points (-3, 1) and (-4, 0) can be found using the slope-intercept form of the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.

To find the slope (m), we use the formula:
m = (y2 - y1) / (x2 - x1)

Substituting the given coordinates:
m = (0 - 1) / (-4 - (-3))
m = (-1) / (-4 + 3)
m = (-1) / (-1)
m = 1

Now that we have the slope (m = 1), we can use one of the points (-3,1) and the slope to find the y-intercept (b).

Using the point-slope form of the equation of a line: y - y1 = m(x - x1)
Substituting the known values:
y - 1 = 1(x - (-3))
y - 1 = 1(x + 3)
y - 1 = x + 3

Rewriting the equation in slope-intercept form:
y = x + 3 + 1
y = x + 4

Therefore, the equation of the line passing through the points (-3,1) and (-4,0) is y = x + 4.