How do you draw the line with the slope #m=1/2# and #y#- intercept #5#?

2 Answers
Apr 15, 2017

Answer:

Start at the y-intercept and count #"rise"/"run"# for the slope.

Explanation:

The equation of the line is #y = 1/2x+5#

You know that the #y#-intercept is at #5#. This is the point where the line crosses the #y#-axis.

Slope is defined as #"y-change"/"x-change" = "vertical"/"horizontal"#

Slope = #1/2# means #2# y units for each #1# x unit.

Starting from the y-intercept at 5:
count UP 1 unit and RIGHT 2 units, mark a point. #(2,6)#
Repeat this process, marking marking points up and to the right.

Starting from the y-intercept at 5:
count DOWN 1 unit and LEFT 2 units, mark a point. #(-2,4)#
Repeat this process, marking marking points down and to the left.

Join the points with a straight line.

graph{1/2x+5 [-19.73, 20.27, -7.08, 12.92]}

Apr 15, 2017

Answer:

#y = 1/2x + 5#

Explanation:

Standard form of an equation of a line is #y = mx + b# where #m# = slope = #(y_2 - y_1)/(m_2 - m_1)# and #b# is the #y#-intercept, which is the point #(0, b)#

Start by plotting the #y#-intercept #(0, 5)#

The slope #m = 1/2#. From the #y#-intercept #(0, 5)#, go up #1, (+y)# and over #2, (+x)# and place a point. Draw a line that passes through the two points.

graph{y = 1/2x + 5 [-9.29, 10.71, 1.32, 11.32]}