Writing a Linear Equation
What is the slope-intercept form of a linear equation?
y = mx + b
functional notation:
f(x) = mx + b
What does the slope of a line represent?
The change in vertical positioning and the change in horizontal positioning over time.
What is the y-intercept of the line y = 5x - 1?
y = mx + b
b = y-intercept = (-1)
Find the slope between the points (0, 0) and (4, 8).
(8-0)/(4-0) = 2
If the graph of f(x) = x shifts up by 3 units, what is the new equation in terms of g(x)?
If f(x) = x,...
"shift up by 3 units" = increase of y intercept
g(x) = x + 3
Write the equation of a line with a slope of 2 and a y-intercept of 3.
y = 2x + 3
Determine the slope of the line that passes through the points (2, 3) and (4, 7).
(7-3)/(4-2) = 4/2 = 2
If the equation of a line is y = -3x + 4, what is the y-intercept?
y = mx + b
b = y-intercept = 4
Given the points (3, 2) and (3, -4), what is the slope?
(-4-2)/(3-3) = -6/0 = undefined because any value divided by zero is undefined.
What happens to the graph of f(x) = x if the slope changes to 2 in terms of h(x)?
"slope changes to 2" = 1m is now 2m
h(x) = 2x
Given the slope of -1 and a y-intercept of 4, what is the equation of the line?
y = -x + 4 or y = 4-x
functional notation:
f(x) = -x + 4 or f(x) = 4-x
If a line goes through the points (1, 2) and (1, 5), what is the slope?
(5-2)/(1-1) = 3/0 = undefined because the quotient of a number and zero is undefined. The line is vertical between these two points.
How can you find the y-intercept from the equation 2y = 6x + 8?
2y = 6x+ 8
(2y)/2 = (6x+8)/2...divide both sides by 2 or multiplying both sides by 1/2
y = 3x + 4
How do you calculate the slope using the points (2, 5) and (6, 1)?
(5-1)/(6-2) = -4/4 = -1
Describe the effect on the graph if the equation changes from f(x) = x to g(x) = x - 5
If f(x) =x...
g(x) = NO CHANGE in slope but shift DOWN by 5 units = x -5
If a line has a slope of 3 and passes through the point (0, -2), write its equation in slope-intercept form.
y = 3x -2
functional notation:
f(x) = 3x - 2
Find the slope of the line given by the equation y = -4x + 2.
y = mx + b
m = slope = -4
Given the equation y = 2/3x + 5, what is the y-intercept?
y = mx + b
b = y-intercept = 5
If a line passes through (1, 1) and (2, 3), what is the slope?
(3-1)/(2-1) = 2/1 = 2
If the graph of f(x) = x shifts down by 2 units, what is the new equation in terms of t(x)?
If f(x) = x
"shifts down by 2 units" = decrease of y-intercept by two units
t(x) = x - 2
Convert the standard form equation 2x + 3y = 6 to slope-intercept form.
y = -2/3x + 2
functional notation:
f(x) = -2/3x + 2
What is the slope of a line that is parallel to the line represented by the equation y = 1/2x + 1?
y = mx + b
m = slope = 1/2...so line parallel is also 1/2
PARALLEL lines have the SAME SLOPE.
Explain is the significance of the y-intercept in a real-world context:
The equation for the relationship between total Time Studying over the previous month (explanatory variable) and Expected Quiz Grade (Response variable) for the month is f(x) = 40 + 15x. Explain is the significance of the y-intercept of this equation.
Explain the process of finding the slope using the coordinates of two points.
- Divide the difference of the two y coordinates of two points by the difference of the two x-coordinates of those same points.
Explain how shifting the graph of f(x) = x to the left affects the equation.
Shifting a graph of a f(x) INCREASES the y-intercept given that the slope remains constant.