Linear Flashcards
What is the standard form of a linear equation?
y = mx + c
In the equation y = mx + c, what does ‘m’ represent?
‘m’ represents the gradient (slope) of the line.
In the equation y = mx + c, what does ‘c’ represent?
‘c’ represents the y-intercept of the line.
What is the y-intercept of a line?
The y-intercept is the point where the line crosses the y-axis.
What is the x-intercept of a line?
The x-intercept is the point where the line crosses the x-axis.
True or False: The gradient of a line is the same as its slope.
True
What is the gradient of a line that goes upwards from left to right?
The gradient is positive.
What is the gradient of a line that goes downwards from left to right?
The gradient is negative.
Fill in the blank: A line is ________ if it has a gradient of 0.
horizontal
Fill in the blank: A line is ________ if it is vertical.
undefined
What does it mean for two lines to be perpendicular?
Two lines are perpendicular if the product of their gradients is -1.
What does it mean for two lines to be parallel?
Two lines are parallel if they have the same gradient.
If the gradient of a line is 3, what is the gradient of a line perpendicular to it?
-1/3
What is the slope of a line represented by the equation 2y - 4x = 8?
The slope is 2.
Convert the equation 3x + 2y = 6 to slope-intercept form.
y = -1.5x + 3
What is the slope of the line represented by the equation y = -4x + 7?
-4
If a line has a slope of 0, what can be said about its direction?
The line is horizontal.
If a line has an undefined slope, what can be said about its direction?
The line is vertical.
True or False: The x-intercept can be found by setting y = 0 in the equation.
True
What is the x-intercept of the line represented by the equation y = 2x - 6?
3
Find the y-intercept of the equation y = 5x + 10.
10
What is the gradient of the line passing through the points (2, 3) and (4, 7)?
2
What formula is used to calculate the gradient between two points (x1, y1) and (x2, y2)?
m = (y2 - y1) / (x2 - x1)
True or False: A line can intersect the x-axis at more than one point.
False
What is the slope of a line that is perfectly horizontal?
0
What is the slope of a line that is perfectly vertical?
undefined
What do you call the point (x, 0) on a graph?
x-intercept
What do you call the point (0, y) on a graph?
y-intercept
If a line has a gradient of 1, what is the angle it forms with the x-axis?
45 degrees
What is the relationship between parallel lines in terms of their slopes?
They have equal slopes.
What is the relationship between perpendicular lines in terms of their slopes?
The product of their slopes is -1.
How can you determine if two lines are parallel from their equations?
Compare their slopes; if they are equal, the lines are parallel.
What is the slope of the line given by the equation 4x + 2y = 8?
-2
What is the y-intercept of the line represented by the equation y = 3x - 5?
-5
What is the significance of the point where a line crosses the y-axis?
It indicates the value of y when x is zero.
Convert the equation y - 2 = 3(x - 1) into slope-intercept form.
y = 3x - 1
