1. write a linear equation to model the situation. you have walked 4 miles on a trail. you continue to walk at a rate of 3 miles per hour for 5 hours.
2. write an equation of the line that passes through the point and has the given slope. write the equation in slope-intercept form.
a. (3,2), m=1/2
b. (-3,2), m=1/2
thanks
I will be happy to critique your thinking. On the first, write the equation for distance walked
1. To write a linear equation to model this situation, we need to determine the relationship between distance, time, and rate. The distance you have walked can be represented by the variable "d" and the time can be represented by the variable "t". The rate at which you are walking is 3 miles per hour, so the equation can be written as:
d = 4 + 3t
Since you have already walked 4 miles, the initial distance is 4, and for every hour you walk at a rate of 3 miles per hour, the distance increases by 3t.
2. To write an equation of the line passing through a given point with a given slope in slope-intercept form (y = mx + b), we can substitute the values of the point (x, y) into the equation and solve for the y-intercept (b).
a. Point: (3, 2), Slope (m) = 1/2
Using the slope-intercept form, we have:
y = mx + b
2 = (1/2)(3) + b
2 = 3/2 + b
To solve for b, we subtract 3/2 from both sides:
2 - 3/2 = b
4/2 - 3/2 = b
1/2 = b
The equation of the line passing through (3, 2) with a slope of 1/2 is:
y = (1/2)x + 1/2
b. Point: (-3, 2), Slope (m) = 1/2
Using the slope-intercept form, we have:
y = mx + b
2 = (1/2)(-3) + b
2 = -3/2 + b
To solve for b, we add 3/2 to both sides:
2 + 3/2 = b
4/2 + 3/2 = b
7/2 = b
The equation of the line passing through (-3, 2) with a slope of 1/2 is:
y = (1/2)x + 7/2