The line presented in the question is . Parallel lines have the same slope. The slope of the presented equation is . Therefore, the answer is:

Remember that when a line is stated as , its slope-intercept conversion has a slope of .

Also bear in mind that we are looking for a parallel line, which means we need to find another line where .

is our answer because , which is what we are looking for.

In order for two lines to be parallel, they must have the same slope and different y-intercepts. In slope-intercept form, the slope of the coefficient of our  value. 

We want to find lines that have a slope of . The two answers that share this slope with the given equation are  and , which correspond with answers A and D. 

Two lines are parallel if and only if they have the same slope. Therefore, we must find the slope of each line. We do this by rewriting each equation in slope-intercept form , with -coefficient  being the slope of the line.

In each case, solve for  by isolating this variable on the left side.

Line A:

The slope of Line A is the -coefficient .

Line B: 

The slope of Line Bis the -coefficient .

Line C: 

The slope of Line C is the -coefficient .

No two of the given lines have the same slope, so no two are parallel.

Two lines are parallel if and only if they have the same slope. Therefore, we must find the slope of each line. We do this by rewriting each equation in slope-intercept form , with -coefficient  being the slope of the line.

In each case, solve for  by isolating this variable on the left side.

Line A:

.

This equation is already in slope-intercept form. The slope of Line A is the -coefficient .

Line B:

The slope of Line B is the -coefficient .

Line C:

The slope of Line C is the -coefficient .

In each case, the slope is . The three lines, having the same slope, are all parallel to one another.

Two lines are parallel if an only if their slopes are equal. The slope of a line with -intercept  and -intercept  can be determined using the formula

.

Calculate the slope of Line A by setting :

Calculate the slope of Line B by setting :

Calculate the slope of Line B by setting :

Lines A and C have the same slope and are parallel; Line B has a different slope and is not parallel to the other two.

First write the equation in slope intercept form. Add  to both sides to get . Now divide both sides by  to get . The slope of this line is , so any line that also has a slope of  would be parallel to it. The correct answer is  .

Using the slope intercept formula, we can see the slope of line p is ¼. Since line k is perpendicular to line p it must have a slope that is the negative reciprocal. (-4/1) If we set up the formula y=mx+b, using the given point and a slope of (-4), we can solve for our b or y-intercept. In this case it would be 17.  

First, you need to obtain the equation of the first line, A. Its slope is given by:

(y₂ - y₁) / (x₂ - x₁) = (1 - 0) / (3 - 0) = 1/3 = slope of A.

Remember that the slope of a perpendicular line to a given line is -1 times the inverse of its slope. Thus the slope of B:

(-1) x 1 / (1/3) = -3

Thus with y = mx + b, m = -3. Now the line must include (3,1). Thus:

  with y = -3x + b:

  1 = -3(3) + b;

  1 = -9 + b; add 9 to both sides:

  10 = b

The given equation is in standard form, so it must be converted to slope-intercept form: y = mx + b to discover the slope is –2/3. To be perpendicular the new slope must be 3/2 (opposite reciprocal of the old slope). Using the new slope and the given point we can substitute these values back into the slope-intercept form to find the new intercept, –5. In slope-intercept form the new equation is y = 3/2x – 5. The correct answer is this equation converted to standard form.