How do you write the equation of a line given (6,-3),(-2,-3)?

3 Answers
Jun 7, 2017

y=-3y=3

Explanation:

First, we need to determine the slope of the line. The slope can be found by using the formula: m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))m=y2y1x2x1

Where mm is the slope and (color(blue)(x_1, y_1)x1,y1) and (color(red)(x_2, y_2)x2,y2) are the two points on the line.

Substituting the values from the points in the problem gives:

m = (color(red)(-3) - color(blue)(-3))/(color(red)(-2) - color(blue)(6)) = (color(red)(-3) + color(blue)(3))/(color(red)(-2) + color(blue)(-6)) = 0/-8 =0m=3326=3+32+6=08=0

Next we can use the point-slope formula to write an equation for the line. The point-slope formula states: (y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))(yy1)=m(xx1)

Where color(blue)(m)m is the slope and (color(red)(x_1, y_1))(x1,y1) is a point the line passes through. Substituting the slope we calculated and the values from the second point in the problem gives:

(y - color(red)(-3)) = color(blue)(0)(x - color(red)(6))(y3)=0(x6)

(y + color(red)(3)) = 0(y+3)=0

y=-3y=3

Jun 7, 2017

y=-3y=3

Explanation:

Begin by finding the slope using the slope formula:
m=(y_2-y_1)/(x_2-x_1)m=y2y1x2x1

Let (6,-3)->(color(red)(x_1),color(blue)(y_1))(6,3)(x1,y1) and (-2,-3)->(color(red)(x_2),color(blue)(y_2))(2,3)(x2,y2)

Find the slope:

m=color(blue)(-3-(-3))/color(red)(-2-6)=0/-8=0m=3(3)26=08=0

The equation of the line can be found using the point-slope formula: y-y_1=m(x-x_1)yy1=m(xx1) where mm is the slope and (x_1,y_1)(x1,y1) is a point on the function. Since we have a slope and two points (we can choose either one. I will use (-2,-3)(2,3)), we can substitute this information like so:

y-(-3)=0(x-(-2))y(3)=0(x(2))

Simplify:

y+3=0x+0y+3=0x+0

y+3=0y+3=0

Write in y=mx+by=mx+b form by isolating the yy

y+cancel(3-3)=0-3

y=-3 <-- Equation of the line

Jun 7, 2017

See a solution process below:

Explanation:

Because both of the y values are the same and equal to color(red)(-3) we know, by definition this is a horizontal line.

Horizontal lines have the form:

y = color(red)(a) where a is the value of y which is the same for each and every value of x.

Therefore, for this problem, an equation is:

y = color(red)(-3)