Search problems

8 problems match “slope of a line”. Clear

Visitors search a sample. Sign in for free to search every problem. Sign in

1. Y-change on a line ●○○○○ 10 ptsMoving along a particular line in the Cartesian plane, when the $x$-value increases by 3 units, the $y$-value increases by 7 units. When the $x$-value increases by 9 units, by how many units will the $y$-value increase?
2. Parameter for a vertical line ●○○○○ 10 ptsGiven points $A(1+a,\,2a)$ and $B(1-a,\,3)$, the angle of inclination of line $AB$ is $90^\circ$. Find $a$.
3. Inclination angle from a direction vector ●○○○○ 10 ptsThe direction vector of the line $l$ has coordinates $(2, 2\sqrt{3})$. Find the inclination angle of the line $l$ in degrees, where the angle lies in $[0^\circ, 180^\circ)$.
4. Angle between two lines ●●○○○ 20 ptsFind the angle between the lines $l_1: \sqrt{3}x - y + 2 = 0$ and $l_2: 3x + \sqrt{3}y - 5 = 0$, in degrees.
5. Second directional derivative of xyz ●●○○○ 20 ptsFind the second directional derivative of $p(x,y,z)=xyz$ at $(2,3,1)$ in the direction of the vector $\mathbf{i}-\mathbf{j}-\mathbf{k}$, using the unit vector $\frac{1}{\sqrt{3}}(1,-1,-1)$ for both directions. Round to two decimal places.
6. Orthocentre of a triangle ●●○○○ 20 ptsFind the coordinates of the orthocentre of the triangle with vertices $A(5,6)$, $B(2,4)$ and $C(1,-3)$. Round each coordinate to two decimal places.
7. Counting lines with acute inclination ●●●○○ 50 ptsLet the line $ax+by+c=0$ have $a$, $b$, $c$ as three different elements of the set $\{-3,-2,-1,0,1,2,3\}$, and suppose the inclination angle of the line is acute. Find the number of distinct such lines.
8. Rotating a line to equal intercepts ●●●○○ 50 ptsThe line $y=10-2x$ is rotated anticlockwise about the origin through an angle $\theta$, where $0 \le \theta \le 90$ (in degrees). The image has $x$-intercept $(p,0)$ and $y$-intercept $(0,q)$. Determine $\theta$ such that $p=q$. Round to two decimal places.