Cab companies often charge a flat fee for picking someone up and then charge an additional fee per mile driven. The city of Raleigh , NC, charges 2.50 fee and 2.50 per mile for each cab ride. For the Raleigh company write an equation in point-slope form to represent the amount charged, C, for m number of miles for the company in Raleigh, NC.
The equation in point-slope form to represent the amount charged, C, for m number of miles for the cab company in Raleigh, NC is:
C = 2.50 + 2.50m
How is an equation written in slope-intercept form the same as point-slope form
An equation in slope-intercept form is written as y = mx + b, where m represents the slope of the line and b represents the y-intercept.
The equation in point-slope form is written as y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
To convert an equation from point-slope form to slope-intercept form, we need to isolate y on one side of the equation. This can be done by distributing the slope (m) to the x term and then adding or subtracting the y-coordinate (y1) from both sides of the equation.
For example, if we have the equation y - 2 = 3(x - 4) in point-slope form, we can distribute the 3 and simplify to get y - 2 = 3x - 12.
Next, we can rearrange the equation to isolate y by adding 2 to both sides: y = 3x - 12 + 2.
Finally, we simplify the equation further: y = 3x - 10.
This equation is now in slope-intercept form, y = mx + b, where the slope (m) is 3 and the y-intercept (b) is -10.
So, although the equation is written in a slightly different form, both the slope-intercept form and point-slope form represent the same linear relationship between variables y and x.