Bunuel wrote:
In the xy-plane, line n passes through the origin and has slope 4. If points (1, c) and (d, 2) are on line n, what is the value of c/d?
A. 0.25
B. 0.5
C. 2
D. 4
E. 8
Though not needed, for the sake of context, the equation of this line in slope intercept form is \(y=4x\) in which \(m\) = slope*
Any line that passes through the origin has one point at (0,0)
We can use slope to find variable values. Slope is defined as \(\frac{rise}{run}=\frac{y_2-y_1}{x2_-x_1}\)
(1) Solve for \(c\) and \(d\).
Use given slope and given points \((1,c)\) and \((d,2)\) and known point \((0,0)\) to solve for \(c\) and \(d\)Careful with placement in the equations:
\(c\), a y-coordinate, goes on top of the fraction
\(d\), an x-coordinate, goes on the bottom
Slope = \(4\)(2) Solve for \(c\) using points
\((1,c)\) and \((0,0)\)
\(\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{c-0}{1-0}=4\)
\(\frac{c}{1}=4\)
\(c=4\)(3) Solve for \(d\) using points
\((d,2)\) and \((0,0)\)
\(\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{2-0}{d-0}=4\)
\(\frac{2}{d}=4\)
\(2=4d\)
\(d=\frac{2}{4}=\frac{1}{2}\)(4) \(\frac{c}{d}=\frac{4}{(\frac{1}{2})}=(4*\frac{2}{1})=8\)
Answer E
*
The slope's equation might make more sense in the context of the equation of the line: \(y=4x\) is derived from y=mx+b. \(m\) = slope and \(b\) = y-intercept. Because \(b\)=0, the \(b\) value is not written. Any line that passes through the origin has the equation \(y=mx\). For line equations, see Bunuel Lines in Coordinate Geometry, here. For more on slope, see Bunuel Slope of a Line, here, and another site, Slope and intercept, here. _________________
—The only thing more dangerous than ignorance is arrogance. ~Einstein—I stand with Ukraine.
Donate to Help Ukraine!