What is the equation of the line in slope-intercept form that passes through (1, 3) and (2, 5)?

Question

Avery Alexander · Accepted Answer

#y = 2x + 1#

To solve this problem we will find the equation using the slope-point formula and then convert to the slope-intercept form.

To use the slope-point formula we must first determine the slope.

The slope can be found by using the formula: #color(red)(m = (y_2 = y_1)/(x_2 - x_1)# Where #m# is the slope and #(x_1, y_1)# and #(x_2, y_2)# are the two points.

Substituting the points we were given allows us to calculate #m# as:

#m = (5 - 3)/(2 - 1)#

#m = 2/1#

#m = 2#

Nest we can use the point-slope formula to obtain the equation for this problem:

The point-slope formula states: #color(red)((y - y_1) = m(x - x_1))# Where #m# is the slope and #(x_1, y_1) is a point the line passes through.

Substituting the slope we calculate and one if the points gives:

#y - 3 = 2(x - 1)#

The slope-intercept form for a linear equation is:

#color(red)(y = mx + c)# where #m# is the slope and #c# is the y-intercept. We can solve the equation we build above for #y# to transform the equation into this format:

#y - 3 = 2x - 2#

#y - 3 + 3 = 2x - 2 + 3#

#y - 0 = 2x + 1#

#y = 2x + 1#