Certainly! To find the equation of a line using the point-slope form, we use the formula:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\((x_1, y_1)\)[/tex] is a point on the line, and [tex]\(m\)[/tex] is the slope of the line.
Given:
- Point: [tex]\((-1, -3)\)[/tex]
- Slope: [tex]\(4\)[/tex]
Let's substitute these values into the point-slope formula:
1. Substitute [tex]\(x_1 = -1\)[/tex], [tex]\(y_1 = -3\)[/tex], and [tex]\(m = 4\)[/tex] into the formula:
[tex]\[ y - (-3) = 4(x - (-1)) \][/tex]
2. Simplify the equation:
[tex]\[ y + 3 = 4(x + 1) \][/tex]
Thus, the equation of the line in point-slope form is:
[tex]\[ y + 3 = 4(x + 1) \][/tex]
From the given options, the correct one is:
[tex]\[ y + 3 = 4(x + 1) \][/tex]
