1.4 Linear Functions and Slope
The slope of a line passing through the points (x1, y1) and (x2, y2) is found by using the slope formula:
Determine the slope of a line passing through each pair of points below.
a) (5, 1) and (3, ­4)
b) (0, 7) and (­3, ­1)
c) (4, ­7) and (4, ­2)
The slope of a line can be positive (line rises to the right), negative (line falls to the right), zero (horizontal line), or undefined (vertical line).
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The equation of a line can be expressed in slope­intercept form as y = mx + b, in point­slope form as y ­ y1 = m(x ­ x1), or in standard form as Ax + By = C. The equation of a line can be written if we know:
a) the slope and y­intercept; e.g. m = 2/3, b = ­7
b) the slope and a point; e.g. m = ­3, point (x1, y1) = (4, ­2)
c) two points on the line; e.g. (x1, y1) = (3, 7) and (x2, y2) = (1, ­1)
2
Examples:
1) Write the equation of a line which passes through the origin and has a slope of ­2/3.
2) Write the equation of a line which has x­intercept 3 and y­intercept ­5.
3) Write the equation of a line which has slope 0 and passes through the point (4, ­7).
4) Write the equation of a line which passes through the points (4, 1) and (­2, 1).
5) Write the equation of a line which passes through the point (3, ­5) and has x­intercept 7.
3
We can easily graph the equation of a line if we know its slope and y­intercept. State the slope and y­intercept of each equation and then graph.
y = 2x ­ 5
y = ­x
Rewrite each equation in slope­intercept form and then state the slope and y­intercept.
a) 4x + y ­ 6 = 0
b) 6x ­ 5y ­ 20 = 0
4
The equation of a horizontal line (slope 0) is y = b, where b is the y­intercept.
The equation of a vertical line (slope undefined) is x = a, where a is the x­intercept.
Graph each equation on the grid provided.
y = 3
x = ­2
y = x
5
Determine the x­intercept and y­intercept of each line whose equation is given, and use these points to graph.
2x ­ 3y = 12
x + y = 5
3x ­ y + 6 = 0
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