Finding the Angle with the X-axis
To find the angle between the graph of a linear equation and the x-axis, we first need to determine the slope of the line. The angle $\theta$ the line makes with the positive x-axis is related to the slope $m$ by the equation $\tan(\theta) = m$. This angle $\theta$ is also called the angle of inclination.
Calculating the Slope
The given linear equation is $35x - 35y + 15 = 0$. We need to rewrite this equation in the slope-intercept form, which is $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept.
- Rearrange the equation to isolate the $y$ term:
$35y = 35x + 15$
- Divide both sides by 35 to solve for $y$:
$y = \frac{35x}{35} + \frac{15}{35}$
$y = 1x + \frac{3}{7}$
- Comparing this with $y = mx + c$, we find that the slope $m = 1$.
Determining the Angle
Now, we use the relationship between the slope and the angle of inclination:
$ \tan(\theta) = m $
Substitute the value of the slope we found:
$ \tan(\theta) = 1 $
To find the angle $\theta$, we take the inverse tangent (arctan) of 1:
$ \theta = \arctan(1) $
The angle whose tangent is 1 is $45^\circ$.
Therefore, the measure of the angle between the graph of the linear equation $35x - 35y + 15 = 0$ and the x-axis is $45^\circ$.
Similar Questions
- Find the relation between x and y such that the point (x, y) is equidistant from (6, 2) and (4, 6).
- The points A (1, 2), B (3, 4) and C (4, 1) are the vertices of a triangle which is:
- The area of the triangle formed by the line $2x - 4y - 7 = 0$ with the coordinate axis is:
- The distance between two points $(a \cos \alpha, 0)$ and $(0, a \sin \alpha)$ is_____.
- Find the area of a triangle formed by $(1, 0)$, $(-1, 0)$, $(0, 1)$.
- Three straight lines $x + y - 3 = 0$, $x + y + 2 = 0$ and $3x + 3y - 7 = 0$ are:
- The image of the point $(7, 8)$ when reflected along the x-axis is:
- The equation of a straight line passing through (-2,5) and (1,3) is:
- The intercepts made by the plane $3x - 4y - 2z = 6$ with the coordinate axis are:
- $\Delta ABC$ is a triangle whose vertices are A(0, 0), B(a, 5) and C(-5, 5). If the triangle is right-angled at A, then find the value of a.
Important Questions from Coordinate Geometry
Find the co-ordinates of the centroid of a triangle whose vertices are A(1, 4), B(7, 8) and C(10, 12).
- If x² + y² - 16x + 38y + 425 = 0, then the value of x² + y² is:
- If x² + y² - 12x + 18y + 117 = 0, then the value of x² + y² is:
- A geological survey team has established three research stations forming a triangular monitoring zone. The stations are located at coordinates P(2,5), Q(8,1), and R(4,9) on a coordinate grid where each unit represents 1 kilometer. What is the area of the triangular monitoring zone?
- \(A(1, 2)\), \(B(a, -26)\), \(C(13, -14)\) and \(D(6, 14)\) are the vertices of a parallelogram, taken in order, find the value of \(a\).
