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

Question

Eli Assouline · Accepted Answer

#y = 1/2x + 5#

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]}

Savannah Anderson · Answer

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

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]}

Eva Abramson · Answer

undefined To draw a line with a slope of $ \frac{1}{2} $ and a y-intercept of 5, you can start by plotting the y-intercept point on the y-axis at y = 5. Then, you can use the slope to determine additional points on the line. Since the slope is $ \frac{1}{2} $, you can interpret it as "rise over run," meaning for every 1 unit increase in the y-direction, there is a 2 unit increase in the x-direction. Therefore, from the y-intercept point (0,5), you can move up 1 unit and to the right 2 units to find another point on the line. Repeat this process to find more points, and then connect them to draw the line.