Write an equation (a) in standard form and (b) in slope-intercept...

Question

Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (1, 6), perpendicular to 3x+5y=1

Accepted Answer

Consider a line defined by six X plus two Y is equals to three. Write the equations both in standard and slope intercept form of a line that is perpendicular to the given line and passes through the 30.25. Now we noticed here, our equation six X Plus two Y is equal to three. As in standard form, we need to change this slope intercept form to determine our slope of our current line to do that you wanna solve for. Why? Let's go ahead and move six x 1st, We then get two Y as equals to negative six X plus three that we can divide by two on both sides to get Y is equals to negative three X plus three FS. We can then tell based on S soap intercept form That the end of our equation is equals to negative three or the slope of our line. Now to find a perpendicular line, you need to find a slope of a line that is perpendicular to this slope. M is equal to negative three. We will take M1 times M2 as equals to eight of one. And so for M2, You know M1 is negative three, M two is some unknown. So that equals to negative one Divided by -3. And both sets, We get M2 as equals to 1/3. So the slope of our perpendicular line is 1/3. Now, we want to find our actual equation of the line. We can do that by using point slope form which tells this Y minus Y one is equals to M times X minus X one Where Y one, X 1 is our point just in reverse order. So Y minus Y one with the Y over point, it's five. Our new slope is 1/3. A one, X -X one or X -2, Y -5 is equals to 1/3, X -2/3. Finally, if we add 5 to both sides, YY is equals to 1/3 x Plus 13/3. Now this is our slope intercept form equation. We also need our standard form equation which standard form is given in the form A XX plus B Y is equal to C. So we need to change our subset form to standard form can do that by moving our X over to the other side. So we have Y as equals to one third, X plus 13/3, subtract our one thirds X, we get negative one thirds X plus Y equals to 13/3. And finally multiply by three on both sides, we get the plus three Y As equals to 13. We want X as positive divided everything by negative one, we get X minus three Y equals to negative 13. We did have both standard form here and slope in form here. We then notice that the only answer that has both of our forms. This answer B OK, I hope to help you solve the problem. Thank you for watching. Goodbye.

Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (1, 6), perpendicular to 3x+5y=1

Key Concepts

Standard Form of a Linear Equation

Slope-Intercept Form

Perpendicular Lines

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