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

Question

Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (-1, 4), parallel to x+3y=5

Accepted Answer

Consider a line defined by two X plus Y equals seven. Write equations both in standard and slope intercept form of a line that is parallel to the given line and passes through the point negative where we have four possible answers all in either standard form or slope intercept form and just various different equations of lines. Now to solve this, let's first find our parallel line slope to do this. We will take our equation two X plus Y equals seven. Now we know standard form is given by A X plus by equals C slope intercept form is given by Y equals MX plus B. Let's transform our current equation into standard form by solving for Y, we can subtract both sides by two X to get Y equals negative two X plus seven. Now we can find our parallel slope for a parallel line. The slope is actually the exact same as our original line. So if M one is our current slope negative two M two will then be the same slope negative two. We can now plug this into our point slip form. Point slope form will help us find slope intercept form if we have the slope of the line and the point that it passes through, we have Y minus Y one equals M multiplied by X minus X one where our point is negative 42, which means we have Y minus two equals negative two, multiplied by X minus negative four, we get Y minus two equals negative two multiplied by X plus four. Now we just see the, so for a while by itself, we can distribute our negative two to get negative two X minus eight and then add two at the end to get Y equals negative two X minus six. Now this is our slope intercept form which we can transform this back in the standard form by moving the X to the other side or standard form. We add two X which gives us two X plus Y is equals to negative six. We now have both standard form and slope intercept form being two X plus Y equals negative six and Y equals negative two X minus six. We can then see the answer to our problem. His answer A 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, 4), parallel to x+3y=5

Key Concepts

Standard Form of a Linear Equation

Slope of a Line and Parallel Lines

Slope-Intercept Form of a Linear Equation

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