write an equation for the line in point slope form...when it passes through (9,1) and the x intercept is 5 and then slope intercept form...im so confused
You have two points identified; (5,0) and (9,1).
The slope of the line passing through these two points is m = (y1-y2)/(x1-x2) or m = (1-0)/(9-4) = 1/4.
Knowing the coordinates of point 1, (9,11), from y = mx + b, 1 = 9/4 + b making b = -5/4.
The line is therefore defined by y = x/4 - 5/4.
Checking:
for x = 5, y = 5/4 - 5/4 = 0.
for x = 9, y = 9/4 - 5/4 = 4/4 = 1.
To write the equation of a line in point-slope form, you need two pieces of information: the slope of the line and a point that it passes through. In this case, we are given that the line passes through the point (9,1) and the x-intercept is 5.
Step 1: Finding the slope
Since we only have the x-coordinate of the x-intercept, we need to find the y-coordinate to calculate the slope. The x-intercept is the point where the line intersects the x-axis, so the y-coordinate must be 0. Therefore, the x-intercept is (5, 0).
The slope (denoted by m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates of the x-intercept (5,0) and the given point (9,1):
m = (1 - 0) / (9 - 5) = 1 / 4
So, the slope of the line is 1/4.
Step 2: Writing the equation in point-slope form
The point-slope form of a line equation is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Using the point (9,1) and the slope 1/4, we have:
y - 1 = 1/4(x - 9)
Step 3: Simplifying to slope-intercept form
To write the equation in slope-intercept form (y = mx + b), where b is the y-intercept, we need to simplify the equation.
First, distribute 1/4 to the terms inside the parentheses:
y - 1 = 1/4x - 9/4
Next, move the constant term (-1) to the other side by adding 1 to both sides:
y = 1/4x - 9/4 + 1
Combining like terms:
y = 1/4x - 9/4 + 4/4
Simplifying the expression:
y = 1/4x - 5/4
Therefore, the equation of the line in slope-intercept form is y = 1/4x - 5/4.