Linear Function

Equation of a line in the slope-intercept form
The equation of a straight line
y=mx+k
is called the slope-intercept form … the form which is solved for y in terms of x.

Intercept
In the slope-intercept form, constant term k is the y-intercept.
• The y-intercept indicates the place where the line crosses the y-axis.


Slope
In the slope-intercept form, the coefficient of x term is the slope.
• The slope of a line means the ratio of the vertical change to the horizontal change between two points on the graph of a line.
slope=
i.e.
slope=
• Especially, when change in x is 1 unit
slope= =(change in y)
Thus,
(for every 1 unit to the right)
slope= the change in y
• When a line goes up left to right it has a positive slope.
When a line goes down left to right it has a negative slope.
Finding the slope with a fraction
When the change of y for the change of 1 x-unit is a fraction, in order to find the slope:
Find two lattice points (points where two grid lines meet) on the line.
Draw a right triangle like a stair step.
From the first point to the second point, think of the vertical change and the horizontal change.
slope=

QuestionFind the equation of the line below.
(Select the correct answer from the right column.)
Graph[1 / 12]


Equations

Correct → , Incorrect →
Result →

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