Step-by-step explanation:
the general slope intercept form is
y = ax + b
a is the slope. it is expressed as ratio of y change / x change when going from one point to another.
b is the y-intercept (the point, where the line crosses the y-axis, meaning the y value when x=0).
we get b by using the point coordinates in the equation and solve for b.
we see costs is on the y axis, and miles is on the x axis.
so what points do we identify on the chart for the green taxi ?
there is right on the y-axis (0, 5). which is already our y-intercept.
and then let's pick e.g. the point where both lines intercept : (3, 8).
for the slope we look at the coordinate changes :
x changes by +3 (from 0 to 3).
y changes by +3 (from 5 to 8).
so, the slope is 3/3 = 1.
and again, the y- intercept is +5.
therefore, the line equation is
y = x + 5
meaning the cost of a fare is the number of miles plus 5.
as alternate interior angles;
as vertical angles;
because point H bisects segment DE (given).