Problem

Write an equation of each line. See Example 3. Ve…

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Problem 40 Hard 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 $\left(\frac{1}{2}, \frac{3}{4}\right)$ and $(0,0)$

Answer

$y=\frac{3}{2} x$

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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 the line that passes through the point 1/2 3 4th and the 0.0 Well, whenever rewrite the equation of the line, the first thing we need to find is this Look. Well, to do that, we're going to use to point the soul formula, which is m equals Y sub two minus y self one over except to minus X of one. So now I'm gonna go back and label my ordered pairs. So from the first order pair, we're gonna have except one. And then why someone? And from the second order pair we have, except to And then why subdue? And now we can substitute these in for our formula, so we'll have m equals why sub two, which is zero minus weiss upon which is 3/4 divided by, except to which is zero minus x of one, which is 1/2. And now we simplify. Well, zero minus 3/4 is negative. Three force and zero minus 1/2 is negative 1/2. Well, this kind of looks a little messy where we have all these fractions. But remember, a fraction just means division, so really, all we have is the fraction negative three Forbes getting to bided by negative 1/2. Well, how do we divide? Fractions will be multiplied by the reciprocal. So we'll have negative 3/4 times negative to over one. And now we can multiply. Well, when we multiply our new Marie, there's negative three times negative to that will give us positive. Six and four times. One is four. Well, we can reduce this by dividing the new Marie there in the denominator by two, which will give us three over to. So now what we found is that our slope is 3/2 now, in this particular case, were given our why intercept? Because we know that our line passes through the 0.0 Keep in mind dusty origin. So the Y intercept in this case will be zero. And now that we know the slope of the Linus tree over to and the Y intercept zero, we can put this in silver intercept form. So we'll have the equation. Why equals 3/2 X plus Cyril Now, with this tree over to exploit zero Well, that's just three over to X. So our final answer will be why equals three over to X

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