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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 $\left(\frac{2}{3}, 2\right)$ and $(0,2)$
2
Algebra
Chapter 3
Graphing Linear Equations and Inequalities in Two Variables; Functions
Section 6
Point–Slope Form
Graphs and Statistics
Equations and Inequalities
Linear Functions
Systems of Equations and Inequalities
Campbell University
University of Michigan - Ann Arbor
Lectures
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and this problem, we're being asked to write the equation of a line that passes through the points 2/3 and two and the order pair zero to well, well, never rewrite the equation of the line. The first thing we need is the slope, which we can find the slope passing through two points using the soul formula, which remember is M equals Y sub two minus. Why someone over, except to mighta sex of one. So now I'm gonna go back and label my ordered pairs. So from the first or two pair, we're gonna have except one. And then why someone? And from the 2nd 1 repair will have except to and then why subdue? And now we're gonna substitute these values into our equation. So we're gonna have m equals Will. Wise up to is to minus y sub one, which is to divided by, except to which is zero minus x of one, which is 2/3 now. We simplify well to minus to a zero and zero minus 2/3 is negative. 2/3 while zero divided by negative 2/3 is just tickled to zero. So now we have a slope of zero which means our line is a horizontal I and remember all horizontal lines take the form of why equals some constant. And the reason why is because all of the Y values for over every ordered pair on that line will have to say, Why value and even know this in our toward repairs? The Y values are both the same. So the equation for our why value will be why equals that constant value for why that they have, which is to sow. Our final answer will be the equation. Why equals two?
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