Question

What is the slope-intercept form equation (y = mx + b) for the given line? Provide the values for m and b.

a) y=3x+7
b) y=−7x−3
c) y=2x−5
d) y=−2x+5

Answer 1

The slope-intercept form of a linear equation is y = mx + b, with m as the slope, and b as the y-intercept. The slope is the rise over run, while the y-intercept is where the line crosses the y-axis. Each given equation shows its specific m and b values.

Step-by-step explanation:

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope of the line, and b is the y-intercept. The slope represents the steepness of the line and is calculated as the rise divided by the run. The y-intercept is the point where the line crosses the y-axis.

For the given options:

• a) y=3x+7 has a slope m = 3 and a y-intercept b = 7.
• b) y=−7x−3 has a slope m = -7 and a y-intercept b = -3.
• c) y=2x−5 has a slope m = 2 and a y-intercept b = -5.
• d) y=−2x+5 has a slope m = -2 and a y-intercept b = 5.

In each case, the coefficient of x provides the slope of the line, and the constant term gives the y-intercept. This allows us to define the shape and position of the line on a graph.