# Explain the summary of slope _intercept equation

## Answers

The slope-intercept form is simply the way of writing the equation of a line so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are immediately apparent. Often, this form is called y = mx + b form. hope this helps pls pls give me brainliest

Step-by-step explanation:

[tex]\boxed{y=\frac{1}{2} x+2}[/tex]

Step-by-step explanation:

Let's take any of the coordinates of blue line to find the slope

The coordinates are (4,4) and (0,2)

Slope = [tex]\frac{y2-y1}{x2-x1}[/tex]

Slope = [tex]\frac{2-4}{0-4}[/tex]

Slope = [tex]\frac{-2}{-4}[/tex]

Slope = m = 1/2

Y-intercept = b = 2 (Because here x= 0)

So, the slope intercept equation becomes:

=> [tex]y = mx+b[/tex]

=> [tex]y = \frac{1}{2} x+2[/tex]

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

[tex]y = \frac{1 }{2}x + 2[/tex]

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

[tex]y = mx + b[/tex]

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.

[tex](x_1, y_1) = (0,2) \\\\(x_2, y_2) = (4,4) \\\\[/tex]

The slope is given by

[tex]m = \frac{y_2 -y_1 }{x_2 -x_1} \\\\m = \frac{4 -2 }{4 -0} \\\\m = \frac{2 }{4} \\\\m = \frac{1 }{2} \\\\[/tex]

The y-intercept is given by

[tex]y = \frac{1 }{2}x + b \\\\2 = \frac{1 }{2}(0) + b \\\\b = 2[/tex]

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

[tex]y = \frac{1 }{2}x + 2[/tex]

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.

[tex]Write the slope-intercept form (y=mx + b) of the blue line. Explain or show your work. Write a one s[/tex]

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y = 1/2x + 2

Comparison: The black and blue line haver the same y-intercept, however they have different slopes. The slope of the black line is 2/3 and the slope of the blue line is 1/2.

Step-by-step explanation:

PLEASE MARK BRAINLIEST

y=1/2x+2(2 is the y-intercept)

The blue line and black line have the same y-intercept, but the black line has a slope 1/6 greater than the blue line.

Hope it helps <3

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