Write an equation in slope-intercept form of a linear function...

Question

Write an equation in slope-intercept form of a linear function f whose graph satisfies the given conditions. The graph of ƒ is perpendicular to the line whose equation is 3x - 2y - 4 = 0 and has the same y-intercept as this line.

Accepted Answer

Hey everyone here we are asked to describe a function in slope intercept form which passes through the point negative 20. It is perpendicular to the line with the equation of five, X minus f of X is equal to negative five. Now we want to start by focusing on finding the slope for the function. And to do this, we first need to get the slope of the given line and so we need to recall that slope intercept form is why is equal to M X plus B. And now we can use this to rearrange the given line so we can clearly see what the slope will be. So we can add F of X to both sides as well as add five to both sides. And this will give us F of X is equal to five X plus five. And now we can clearly see that the slope for the line is five, which I will denote as M sub one. And now, since the line is perpendicular to the function we can use the formula M sub one times M sub two is equal to negative one. In order to find the slope for the function. Now we can plug in our slope for the line which gives us five times M sub two is equal to negative one, dividing both sides by five. We see that the slope for the function is negative 1/5. And now from here we see that we are given one point and we now have the slope. So we can write the equation for the function in point slope form recalling point slope form. It is why minus Y. Sub one is equal to slope and times the quantity of x minus x. Sub one. And now we can just plug in our information that we have. So we have y minus Y. Sub one which is zero is equal to M. Which we found to be negative 1/5 Times The Quantity of X -X one which is -2. And now from here we want to get this equation into slope intercept form. So we just need to simplify and factor in this negative 1/5. So we have Y is equal to negative 1/5 X plus negative 1/5 times two. And now we can also write why since it is a function we can write it as a function of X or X. So we have F of X is equal to negative 1/5 x minus 2/5. And that is our final answer here for choice D Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Write an equation in slope-intercept form of a linear function f whose graph satisfies the given conditions. The graph of ƒ is perpendicular to the line whose equation is 3x - 2y - 4 = 0 and has the same y-intercept as this line.

Key Concepts

Slope-Intercept Form

Perpendicular Lines

Finding the Y-Intercept

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