What is the equation of the line that passes through the point \( (-4,-5) \) and has a slope of 2 ?

To find the equation of the line, you can use the point-slope form, which is written as \( y - y_1 = m(x - x_1) \). Plugging in the point \( (-4, -5) \) for \( (x_1, y_1) \) and the slope \( m = 2 \), we have: \( y - (-5) = 2(x - (-4)) \) This simplifies to: \( y + 5 = 2(x + 4) \) Expanding and solving, we get: \( y + 5 = 2x + 8 \) So, the equation of the line in slope-intercept form is \( y = 2x + 3 \). You just created the equation of a line that captures both its steepness with a slope of 2 and the specific point where it crosses through! This form is super handy because you now know the y-intercept is 3, which means it crosses the y-axis at that point. As you work on understanding lines, keep in mind that practicing with points and slopes helps you visualize how lines behave on a graph. You can even try drawing it out to see how the slope affects the angle of the line!