Problem

Find an equation of the line that passes through …

01:41

Problem 36 Medium Difficulty

Find an equation of the line that passes through the two given points. Write the equation in slope-intercept form, if possible. See Example 2.
Passes through $(-3,0)$ and $(3,1)$

Answer

$\frac{x}{6}+\frac{1}{2}$

Related Courses

Algebra

Elementary and Intermediate Algebra

Chapter 3

Graphing Linear Equations and Inequalities in Two Variables; Functions

Section 6

Point–Slope Form

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Video Transcript

we're being asked to write the equation of a line that passes through the two points Negative 30 and 31 Well, we'll never rewrite the equation of the line. The first thing we need is the soap of the line. Well, the find the soap of online. We're gonna use the slope formula, which remember is m equals y sub too, minus y someone all over, except to minus six of one. So I'm gonna go back and label my ordered pairs. So for my first started pair, I'll have except one. Then why someone and then accept to wise up to. And I'm going to substitute these values into my equation. So we'll have equals Weiss of two, which is one minus y sub one, which is zero divided by, except to which is three minus x of one, which is negative three and now will simplify, while one minus zero is one and three minus negative. Three is six. So now we found the slope to be won over six. Now, because we are not given the y interest up, we need to use point slope form to write the equation of this line will remember a point slope form is the equation. Why, minus y someone equals m times the quantity of X minus except one. Well, to use this form, the first thing we need is to slope which were given. That's our M value. We also need X of one and Weiss of one, which is just a point on our line, will remember. We already labeled our first ordered pair ex of one Weiss of one. So we can use that and substitute those values into this equation. So what are we gonna have? Well, we're gonna have y minus why someone which is zero equals m, which we found to be won over six times to quantity of X minus x of one, which is negative. Three. Now, we're being asked to make sure our final answer isn't slope intercept for meaning that why is already by itself. So on the left hand side, No, this we have y minus zero. Well, that's just equal to why, And on the right hand side. No, this inside Our preface is we have two negatives extra. Each upper well, that will become a positive. So we'll be left with 1/6 times. to quantity of X plus three. So now to put this in slope intercept form, we simply need to distribute the 16 x So we'll have y equals well, 1/6 times X is 1/6 x and 1/6 times three is positive 1/2 and now our equation is in slope intercept form. So the equation for this line is why equals 1/6 x plus 1/2.

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