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 are given two points
(9,1) and (5,0)
Every textbook must have an example for this basic type of question.
thanks drwls...and wow thanks for nothing reiny ..you sound like a know it all so sorry i didn't know what to do never mind im not..no need to be a jerk bout it....
To write the equation of a line in point-slope form, you need to know the slope of the line and the coordinates of a point on the line. Similarly, to write the equation of a line in slope-intercept form, you need to know the slope of the line and the y-intercept. Let's go step by step.
Step 1: Find the slope of the line.
You have been given that the x-intercept is 5. The x-intercept is the point where the line crosses the x-axis, and it has the form (x, 0). In this case, the x-intercept is (5,0).
To find the slope of the line, you can use the formula:
slope = (change in y) / (change in x)
Since the line passes through the x-intercept (5,0) and the point (9,1), you can calculate the slope as:
slope = (1 - 0) / (9 - 5)
= 1 / 4
= 0.25
Step 2: Write the equation in point-slope form.
The point-slope form of a linear equation is given by:
y - y₁ = m(x - x₁)
Substituting the values we know, with (x₁, y₁) as (9,1) and m as 0.25:
y - 1 = 0.25(x - 9)
This is the equation in point-slope form.
Step 3: Convert the equation to slope-intercept form.
The slope-intercept form of a linear equation is given by:
y = mx + b
To convert the equation to slope-intercept form, you can rearrange it by isolating y:
y - 1 = 0.25(x - 9)
y - 1 = 0.25x - 2.25
y = 0.25x - 1.25
This is the equation in slope-intercept form.
So, the equation of the line passing through the point (9,1) with an x-intercept of 5 is y = 0.25x - 1.25.
The line passes through (9,1) and (5,0)
The slope is (1-0)/(9-5) = 1/4
y = (1/4) x + b
1 = 9/4 + b
b = -5/4
y = (1/4)(x - 5)
is the equation of the line.