In Exercises 11–38, use the given conditions to write an equation...

Question

In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. x-intercept = -1/2 and y-intercept = 4

Accepted Answer

Hey everyone here we are asked to write an equation for the line in slope intercept form by first going through point slope form. So we want to start by noting our given intercepts and writing them as ordered pairs. So starting with our x intercept of 1/5 it is an X intercept. So the y coordinate must be zero. So we have the ordered pair of 1/5 0 next with our Y intercept of 10, it is a Y intercept. So the X coordinate must be zero. So we have the 00.0 10. Now from here we can start looking for our slope. So we need to recall the slope formula which is that slope M is equal to the quantity of Y sub two minus Y sub one divided by the quantity of X sub two minus X sub one. Now from here we need to assign our points as either X and one Y sub one or accept two, Y sub two. So I'm going to let our x intercept B the X one and Y sub one point. And then our Y intercept must be except two and Y sub two. So it is important to note that it doesn't matter which point is assigned what as long as it's kept consistent throughout the problem. So we can now plug in this information into our slope formula. So in the numerator we have Y sub two which is 10 minus Y sub one which is zero. And in the denominator we have X sub two which is zero minus X sub one which is 1/5. And from here we can just simplify. So 10 minus zero is just 10 divided by zero minus 1/5 which is negative 1/5 and 10 divided by negative 1/5 is the same as 10 times negative five. So we have a slope of negative 50. And so next we need to recall our point slope form which is why I minus Y. Sub one is equal to m times the quantity of x minus X. Of one. And now we can just plug in all of the information we have. So we have the form y minus Y sub one which is zero is equal to M. Which we found as negative 50 times the quantity of x minus X. Of one which is 1/5. So now we can just simplify and we want to factor in this negative 50 to get our equation into slope intercept form. So we now have the slope intercept form of Y is equal to negative 50 times x plus negative 50 times negative 1/5 which is positive 10. So we have a final answer of why is equal to negative 50 X plus 10 which is our answer here for choice. D Thanks for watching. I hope you found this video helpful and I'll see you again next time

In Exercises 11–38, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. x-intercept = -1/2 and y-intercept = 4

Key Concepts

Point-Slope Form

Slope-Intercept Form

Intercepts

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