Find the Linear Function Through (-3,-5) with 45-Degree Angle

Question

Which function represents a straight line that passes through the point $(-3,-5)$ and creates an angle of 45 degrees with the positive part of the x axis?

Video Solution

Solution Steps

00:00 Find the algebraic representation of the function

00:03 We'll use the formula to calculate slope according to the angle with X-axis

00:07 We'll substitute the angle according to the given data and calculate to find the slope

00:17 This is the line's slope

00:22 Now we'll use the line equation

00:26 We'll substitute the point according to the given data

00:31 We'll substitute the slope and solve to find the intersection point (B)

00:49 We'll isolate the intersection point (B)

00:53 This is the intersection point with Y-axis

00:58 Now we'll substitute the intersection point and slope in the line equation

01:09 And this is the solution to the question

Step-by-Step Solution

To solve this problem, let's start by finding the slope $m$ of the line. Since the line makes a 45-degree angle with the positive $x$ -axis, the slope $m = \tan(45^\circ) = 1$ .

Next, we will use the point-slope form of the line equation, which is given by:

$y - y_1 = m(x - x_1)$

where $(x_1, y_1) = (-3, -5)$ and $m = 1$ . Substituting these values, we have:

$y + 5 = 1 \cdot (x + 3)$

which simplifies to:

$y + 5 = x + 3$

Subtract 5 from both sides to put it into slope-intercept form $y = mx + b$ , we get:

$y = x - 2$

Therefore, the function that represents the line through $(-3, -5)$ with a 45-degree angle with the $x$ -axis is $y = x - 2$ .

Answer

$y=x-2$

Related Subjects

Finding a Linear Equation

Question Types

Equation of a Straight Line: Using the angle formed by the line with the axes