How do you use a system of equations to find the equation of a line, in slope-intercept form that contains the given points, (-2, 1) and (8,1)?

Question

Avery Alexander · Accepted Answer

See the full solution process below.

Because both points have the same #y# value we know this line is a vertical line. a vertical line has the formula: #y = y_1# or in this case #y = 1# The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)# In this case, because there is no #x# term in the equation the slope must be #0# and we know the y-intercept is #1#. Therefore the slope-intercept form of the equation for this line is: #y = color(red)(0)x + color(blue)(1)#

Savannah Anderson · Answer

undefined To find the equation of a line in slope-intercept form that contains the given points (-2, 1) and (8, 1), we can first determine the slope using the formula $ m = \frac{y_2 - y_1}{x_2 - x_1} $. Substituting the coordinates (-2, 1) and (8, 1), we get $ m = \frac{1 - 1}{8 - (-2)} = \frac{0}{10} = 0 $. Since the slope is 0 and the line passes through the point (8, 1), the equation of the line is $ y = 1 $.