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124319
11.01.2022 •
Mathematics
What is the equation of the line that passes through the points (4,3),(6,5)?
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Ответ:
Skills needed: Point-slope Form
Step-by-step explanation:
1) First, let's try to make sense out of the problem. We are given two coordinate points and have to create a line out of it.
---> The most efficient way to solve this is with point-slope form.
The point slope form, given One coordinate point and Slope is:
Given coordinate pair
and Slope ![m](/tpl/images/2615/3123/d8537.png)
--->![y-y_1=m(x-x_1)](/tpl/images/2615/3123/8dd46.png)
2) Now, we have one coordinate pair/point, but we need slope.
---> The slope is the rate of change, and can be found with a formula:
Given two coordinate points
and
, the slope is:
--->![\frac{y_2-y_1}{x_2-x_1}](/tpl/images/2615/3123/f6758.png)
Let's use this formula for the points above:
Based on the above: Slope = 1 (or
)
3) Next, we use point slope form. Let's use coordinate pair (4, 3) -- It does not matter which one:
The 1 does not mean anything (since anything multiplied by 1 is itself, so it can be taken out:
Now to get it to slope-intercept form (
) ---> We add 3 to both sides
--->![y-3+3=x-4+3 \\ y=x-1](/tpl/images/2615/3123/e4d52.png)
y=x-1 is the final equation.
Ответ: