What is the y - intercept of the line that goes through the points (4,3) and (8,2) ?
First, we need to find the slope of the line:
slope = (change in y) / (change in x)
slope = (2 - 3) / (8 - 4)
slope = -1/4
Now we can use the point-slope formula to find the equation of the line:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is one of the given points. Let's use (4,3):
y - 3 = (-1/4)(x - 4)
Simplifying:
y = (-1/4)x + 4 + 3
y = (-1/4)x + 7
The y-intercept occurs when x = 0, so we can substitute that into the equation to find the y-intercept:
y = (-1/4)(0) + 7
y = 7
Therefore, the y-intercept of the line that goes through the points (4,3) and (8,2) is 7.
To find the y-intercept of the line, we need to determine the equation of the line first using the given points.
Step 1: Calculate the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
Given points: (4,3) and (8,2)
Applying the formula:
m = (2 - 3) / (8 - 4)
m = -1 / 4
Step 2: Use the slope-intercept form of the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.
Substituting the given slope (m) and one of the points (x, y), let's use the point (4, 3):
3 = (-1/4) * 4 + b
Step 3: Solve for b (the y-intercept):
3 = -1 + b
b = 3 + 1
b = 4
Therefore, the y-intercept of the line that passes through the points (4,3) and (8,2) is 4.