What is 3x + 4y = 8 in slope-intercept form?
2 answers:
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We could use the formula, derive the formula, or just work it out for this case. Let's do the latter.
The distance of a point to a line is the length of the perpendicular from the line to the point.
So we need the perpendicular to 5x-4y=10 through (-1,3). To get the perpendicular family we swap x and y coefficients, negating one. We get the constant straightforwardly from the point we're going through:
4x + 5y = 4(-1)+5(3) = 11
Those lines meet at the foot of the perpendicular, which is what we're after.
4x + 5y = 11
5 x - 4y = 10
We eliminate y by multiplying the first by four, the second by five and adding.
16x + 20y = 44
25x - 20y = 50
41x = 94
x = 94/41
y = (11 - 4x)/5 = 15/41
We want the distance from (-1,3) to (94/41,15/41)
<em><u>Equation shows the relationship between distance traveled (d), speed (s), and time taken (t) is:</u></em>
<em><u>Solution:</u></em>
Given that,
Alice traveled 30 miles in 3 hours
<em><u>To find: Equation shows the relationship between distance traveled (d), speed (s), and time taken (t)</u></em>
<em><u>The speed is given by:</u></em>
From given,
Distance = d = 30 miles
Time = t = 3 hours
Therefore,
Thus the equation is found and speed is calculated