Answer:
3. b) y = (1/2)x + 1
3. c) y = -2x
3. d) y = -2x + 3
Step-by-step explanation:
The equation of a line is y = mx + b.
x and y are points on the graph.
m is the slope.
b is the y-intercept.
When a slope is negative, it is a negative value (like -1, -7 or -2/3). When a slope is positive, it is a positive value (like 1, 7 or 2/3).
When a line is steep, is has a greater slope and a greater slope value in an equation. (Think about hiking: a steeper hill is harder to climb. The floor is least steep with a slope of about 0.)
The y-intercept occurs when x = 0. On a graph, the line hits the y-axis.
In the equation y = x, the slope is 1.
3. b
The slope is half as that of the line y = x. Half of 1 is 1/2.
m = 1/2 <=this number is positive already
We know the y-intercept is 1 because x=0 in the point.
Put the slope and y-intercept back into the equation:
y = (1/2)x + 1
3. c
The slope is twice as that of the line y = x. Double of 1 is 2.
m = 2 <=this number needs to be negative. m = -2
We know the y-intercept is 0 because x=0 in the point. We do not need to write the y-intercept if it's 0.
Put the slope into the equation:
y = -2x
3. d
The slope is half as that of the line y = x. Half of 1 is 1/2.
m = 1/2 <=this number needs to be negative. m = -1/2
The given point, (0,3), shows the y-intercept is 3 because x = 0.
Put the slope and y-intercept back into the equation:
y = -2x + 3
