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

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?

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 $y = x - 2$.