Question
Sketch the graph of y = 3x - 6
Hint:
A linear equation is in the form ax + by + c = 0. A graph is a geometrical representation of an equation. A coordinate point (x, y) consists of the distance from the horizontal and vertical axis as coordinates.
We are asked to sketch the graph of the given equation.
The correct answer is: y = - 3
Step 1 of 2:
Find two coordinate points of the equation;
When x = 0,
y = 3x - 6
y = 3(0) - 6
y = 0 - 6
y = - 6
When x = 1,
y = 3x - 6
y = 3(1) - 6
y = 3 - 6
y = - 3
Thus, the required points are:
Step 2 of 2:
Plot the points and join them to get the required graph of the equation.
Thus, the graph is:
We only require just two coordinate points to graph a linear equation in two variables. In case of a quadratic equation we would need at least three coordinate points.
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¶The formula for equations of a line is:
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2) The equation y = mx + b for the slope-intercept
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Write the equation in slope-intercept form of the line that passes through the points (3, 1) and (0, -3).
The slope-intercept form of a line is the most common way to express a line's equation. For example, the slope-intercept form, y = mx + c, is the equation of a straight line with slope m and intercept c on the y-axis. In this case, m and c can be any two real numbers.
The value of m in the equation defines the line's slope (or gradient). It can have a positive, negative, or 0 value.
• Positive gradient lines rise from left to right.
• Negative gradient lines slant in reverse order From left to right.
• The gradient of horizontal lines is zero.
The value of c is known as the line's vertical intercept. When x = 0, this is the value of y. When drawing a line, c indicates where the line intersects the vertical axis.
For example, y = 3x + 2 has a slope of 3 (i.e., m = 3) and an intercept of 2 on the y-axis (i.e., c = 2).
To determine the slope-intercept equation. First, find the slope of a line and then the y-intercept of a line.
Write the equation in slope-intercept form of the line that passes through the points (3, 1) and (0, -3).
The slope-intercept form of a line is the most common way to express a line's equation. For example, the slope-intercept form, y = mx + c, is the equation of a straight line with slope m and intercept c on the y-axis. In this case, m and c can be any two real numbers.
The value of m in the equation defines the line's slope (or gradient). It can have a positive, negative, or 0 value.
• Positive gradient lines rise from left to right.
• Negative gradient lines slant in reverse order From left to right.
• The gradient of horizontal lines is zero.
The value of c is known as the line's vertical intercept. When x = 0, this is the value of y. When drawing a line, c indicates where the line intersects the vertical axis.
For example, y = 3x + 2 has a slope of 3 (i.e., m = 3) and an intercept of 2 on the y-axis (i.e., c = 2).
To determine the slope-intercept equation. First, find the slope of a line and then the y-intercept of a line.
what values must be restricted from the domain for x ?
