Final answer:
To determine the linear equation in slope-intercept form for the taxi fare in Detroit, we calculate the slope from two given points resulting in $3.50 per mile, and derive the y-intercept as $4. The resulting equation is y = $3.50x + $4.
Step-by-step explanation:
To write the equation for the taxi fare in Detroit in slope-intercept form (y = mx + b), we need to determine both the slope (m) and the y-intercept (b). Given that a 2-mile ride costs $11 and a 4-mile ride costs $18, we first calculate the slope, which is the rate of change in fare with respect to miles.
We have two points (2, $11) and (4, $18), and the slope m is calculated as follows:
m = (y2 - y1) / (x2 - x1) = ($18 - $11) / (4 - 2) = $7 / 2 = $3.50
The slope (m) indicates that the fare increases by $3.50 for each additional mile. Applying one of the points to the slope-intercept formula along with the slope, we can find the y-intercept (b). Using the point (2, $11):
$11 = $3.50(2) + b
This gives us:
b = $11 - $7 = $4
So the y-intercept is $4, representing the initial fare price before any distance is covered. Finally, the equation in slope-intercept form that represents the situation is:
y = $3.50x + $4