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Find the equation of the line that satisfies the given conditions.

(a) Write the equation in standard form.

(b) Write the equation in slope-intercept form.

x-intercept (1,0); slope 2

The standard form of the eauation is....?

The slope-intercept form of the equation is y=....?

Explanation and answers?

 Oct 31, 2014

Best Answer 

 #1
avatar+130511 
+5

 

 

 

We have a slope (2) and a point (1, 0)

We could use something known as the point - slope equation to get to the slope-intercept form, but here's a faster way. Note that, if the slope is 2, this means that everytime x changes by a positive 1, y changes by a positive 2. And everytime x changes by a negative 1, y changes by a negative 2. So, when x changes from 1 to 0, it changes by a negative 1, so y changes by negative 2.... from 0 to -2. So (0, -2) is on the graph...so the y intercept is at -2.

So......the slope intercept form  is given by:

y = mx + b     where m is the slope and b is the y intercept.   So we have

y = 2x - 2     and that's slope-intercept form

To get standard form, get x and y on one side of the equation and the constant on the other

So we have   (noting that y  = 1y)

 y = 2x - 2   or  1y = 2x - 2           subtract 1y from both sides  and add 2 to both sides....so we have,,,

2 = 2x - 1y     or      2x - 1y = 2       and that's standard form

 

 Oct 31, 2014
 #1
avatar+130511 
+5
Best Answer

 

 

 

We have a slope (2) and a point (1, 0)

We could use something known as the point - slope equation to get to the slope-intercept form, but here's a faster way. Note that, if the slope is 2, this means that everytime x changes by a positive 1, y changes by a positive 2. And everytime x changes by a negative 1, y changes by a negative 2. So, when x changes from 1 to 0, it changes by a negative 1, so y changes by negative 2.... from 0 to -2. So (0, -2) is on the graph...so the y intercept is at -2.

So......the slope intercept form  is given by:

y = mx + b     where m is the slope and b is the y intercept.   So we have

y = 2x - 2     and that's slope-intercept form

To get standard form, get x and y on one side of the equation and the constant on the other

So we have   (noting that y  = 1y)

 y = 2x - 2   or  1y = 2x - 2           subtract 1y from both sides  and add 2 to both sides....so we have,,,

2 = 2x - 1y     or      2x - 1y = 2       and that's standard form

 

CPhill Oct 31, 2014

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