Certainly! To find the equation of a line passing through a point and with a given slope, we typically use the point-slope form of the equation of a line. The point-slope form is given by:
[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.
In this case, we have the point [tex]\((-5, 4)\)[/tex] and the slope [tex]\(m = -6\)[/tex].
Step 1: Substitute the given point and slope into the point-slope form.
[tex]\[ y - 4 = -6(x + 5) \][/tex]
Step 2: Simplify the equation to slope-intercept form [tex]\(y = mx + b\)[/tex].
To do that, we expand the right-hand side and solve for [tex]\(y\)[/tex]:
[tex]\[ y - 4 = -6(x + 5) \][/tex]
Distribute the [tex]\(-6\)[/tex]:
[tex]\[ y - 4 = -6x - 30 \][/tex]
Next, isolate [tex]\(y\)[/tex] by adding 4 to both sides of the equation:
[tex]\[ y = -6x - 30 + 4 \][/tex]
Simplify the constants on the right-hand side:
[tex]\[ y = -6x - 26 \][/tex]
Conclusion:
The equation of the line in slope-intercept form is:
[tex]\[ y = -6x - 26 \][/tex]
