Question

Write the slope-intercept form (y=mx + b) of the blue line. Explain or show your work. Write a one sentence summary comparing the blue line to the black line. Hint: Find the y-intercept. Then count up and over (y/x) to the next point on the line to determine the slope.

Answer 1

Answer:

Therefore, the slope-intercept form of the blue line is

$y = \frac{1 }{2}x + 2$

Comparison:

The blue and black lines both have equal y-intercept but different slopes.

The black line is steeper than blue line which means the black line has a greater slope than the blue line.

Step-by-step explanation:

Please refer to the attached graph of this question where we have two straight lines.

The slope-intercept form is given by

$y = mx + b$

Where m is the slope of the line and b is the y-intercept.

Let us find the slope of the blue line from the points given in the graph.

$(x_1, y_1) = (0,2) \\\\(x_2, y_2) = (4,4)$

The slope is given by

$m = \frac{y_2 -y_1 }{x_2 -x_1} \\\\m = \frac{4 -2 }{4 -0} \\\\m = \frac{2 }{4} \\\\m = \frac{1 }{2}$

The y-intercept is given by

$y = \frac{1 }{2}x + b \\\\2 = \frac{1 }{2}(0) + b \\\\b = 2$

Therefore, the slope-intercept form of the blue line is

$y = \frac{1 }{2}x + 2$

Comparison:

The blue and black lines both have equal y-intercept but different slopes.

The black line is steeper than blue line which means the black line has a greater slope than the blue line.