Write an equation for each line described. Give answers in sta...

Question

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-2,5) having slope -4

Accepted Answer

Welcome back. I am so glad you're here. We are asked to find the equation of a line passing through a point negative 49 and having a slope equal to negative eight. And we are to write the equation in slope intercept form. Well, we recall from previous lessons that slope intercept form is Y equals MX plus B where M is the slope and B is the Y intercept. So let's look back at the practice problem and see what we're given. Well, we're given this point negative 49, but that's not the white intercept. We do have the slope, the slope is equal to negative eight, but we don't have the Y intercept. So we can't jump right in with slope intercept form. We need to use a different equation for a little bit first. So we're going to start off using point slope form because we have a point and the slope, we recall from previous lessons, that point slope form is Y minus Y one equals M times parentheses X minus X one. And so we bring down the Y minus part and then we look and see what, why one is. Well, in our point, we have X one comma why one? And X one is negative four, Y one is nine. So we can plug nine in to our point slope form. And then we know what our M is. Our M is negative eight. And then we go back to plugging in -101 is -4. Now, we can simplify this. So we have bringing down why -9 that stays equals, we have negative eight times x minus negative four is going to be plus four. Now, what's in the parentheses is simplified and we can go and distribute this negative eight to the X and the four bringing down our Y minus nine, negative eight times X is negative eight X negative eight times four is minus 32. And now for our desired slope intercept form, why is by itself on one side of the equation? So let's make that happen. Let's get why by itself will add nine to both sides. So then on the left, we have Y equals good. That's what we want. We have negative eight X, that's good. We have our slope of negative eight in front of the X and this is negative 32 plus nine, which is going to be a minus 23. And now this is in the format of Y equals M X plus B. So we look at our answer choices for Y equals negative eight X minus 23. And that matches with answer choice. B well done. We'll catch you on the next one.

Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. through (-2,5) having slope -4

Key Concepts

Slope of a Line

Point-Slope Form of a Line

Standard and Slope-Intercept Forms of a Line

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